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th

In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity property of coherent risk measures is dispensed with and positive homogeneity is weakened, include all practically used risk measures, in particular, both convex risk measures and Value-at-Risk. From a financial viewpoint, our relaxation of convexity is necessary to quantify the capital requirements for risk exposure in the presence of liquidity risk, competitive delegation, or robust aggregation mechanisms. From a decision theoretical perspective, star-shaped risk measures emerge from variational preferences when risk mitigation strategies can be adopted by a rational decision maker.

Star-shaped Risk Measures

2021-03-29 20:33:10

Erio Castagnoli, Giacomo Cattelan, Fabio Maccheroni, Claudio Tebaldi, Ruodu Wang

http://arxiv.org/abs/2103.15790v3, http://arxiv.org/pdf/2103.15790v3

econ.TH

th

In this study, we consider the real-world problem of assigning students to classes, where each student has a preference list, ranking a subset of classes in order of preference. Though we use existing approaches to include the daily class assignment of Gunma University, new concepts and adjustments are required to find improved results depending on real instances in the field. Thus, we propose minimax-rank constrained maximum-utility matchings and a compromise between maximum-utility matchings and fair matchings, where a matching is said to be fair if it lexicographically minimizes the number of students assigned to classes not included in their choices, the number of students assigned to their last choices, and so on. In addition, we also observe the potential inefficiency of the student proposing deferred acceptance mechanism with single tie-breaking, which a hot topic in the literature on the school choice problem.

Optimal class assignment problem: a case study at Gunma University

2021-03-31 11:02:38

Akifumi Kira, Kiyohito Nagano, Manabu Sugiyama, Naoyuki Kamiyama

http://arxiv.org/abs/2103.16879v1, http://arxiv.org/pdf/2103.16879v1

cs.GT

th

We study the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup (Bolton and Harris (1999)), where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences a la Hansen and Sargent (2001), thus we frame the decision making environment as a two-player differential game against nature in continuous time. We characterize the DM value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. We then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, we show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion.

Robust Experimentation in the Continuous Time Bandit Problem

2021-03-31 23:42:39

Farzad Pourbabaee

http://dx.doi.org/10.1007/s00199-020-01328-3, http://arxiv.org/abs/2104.00102v1, http://arxiv.org/pdf/2104.00102v1

econ.TH

th

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We also reduce the dimension of the problem by classifying banks according to different types, in an appropriate type space. These types may be calibrated to real-world data by using machine learning techniques. We then state various limit theorems regarding the final size of default cascade over different types. In particular, under suitable assumptions on the degree and threshold distributions, we show that the final size of default cascade has asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions and show how the systemic risk measure, in a given stress test scenario, could be related to the structure and heterogeneity of financial networks. We finally show how these results could be used by a social planner to optimally target interventions during a financial crisis, with a budget constraint and under partial information of the financial network.

Limit Theorems for Default Contagion and Systemic Risk

2021-04-01 07:18:44

Hamed Amini, Zhongyuan Cao, Agnes Sulem

http://arxiv.org/abs/2104.00248v1, http://arxiv.org/pdf/2104.00248v1

q-fin.RM

th

In real life auctions, a widely observed phenomenon is the winner's curse -- the winner's high bid implies that the winner often over-estimates the value of the good for sale, resulting in an incurred negative utility. The seminal work of Eyster and Rabin [Econometrica'05] introduced a behavioral model aimed to explain this observed anomaly. We term agents who display this bias "cursed agents". We adopt their model in the interdependent value setting, and aim to devise mechanisms that prevent the cursed agents from obtaining negative utility. We design mechanisms that are cursed ex-post IC, that is, incentivize agents to bid their true signal even though they are cursed, while ensuring that the outcome is individually rational -- the price the agents pay is no more than the agents' true value. Since the agents might over-estimate the good's value, such mechanisms might require the seller to make positive transfers to the agents to prevent agents from over-paying. For revenue maximization, we give the optimal deterministic and anonymous mechanism. For welfare maximization, we require ex-post budget balance (EPBB), as positive transfers might lead to negative revenue. We propose a masking operation that takes any deterministic mechanism, and imposes that the seller would not make positive transfers, enforcing EPBB. We show that in typical settings, EPBB implies that the mechanism cannot make any positive transfers, implying that applying the masking operation on the fully efficient mechanism results in a socially optimal EPBB mechanism. This further implies that if the valuation function is the maximum of agents' signals, the optimal EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave valuations, which include weighted-sum valuations and l_p-norms, the welfare optimal EPBB mechanism obtains half of the optimal welfare as the number of agents grows large.

Cursed yet Satisfied Agents

2021-04-02 04:15:53

Yiling Chen, Alon Eden, Juntao Wang

http://arxiv.org/abs/2104.00835v4, http://arxiv.org/pdf/2104.00835v4

cs.GT

th

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible agents. We translate the wedge, cone, and suspension operations into the language of political structures and show how these constructions correspond to merging structures and introducing mediators. We introduce the notions of the viability of an agent and the stability of a political system and examine their interplay with the simplicial complex topology, casting their interactions in category-theoretic language whenever possible. We introduce a refinement of the model by assigning weights to simplices corresponding to the number of issues the agents agree on. In addition, homology of simplicial complexes is used to detect non-viabilities, certain cycles of incompatible agents, and the (non)presence of mediators. Finally, we extend some results from [1], bringing viability and stability into the language of friendly delegations and using homology to examine the existence of R-compromises and D-compromises.

Political structures and the topology of simplicial complexes

2021-04-05 23:07:35

Andrea Mock, Ismar Volic

http://arxiv.org/abs/2104.02131v3, http://arxiv.org/pdf/2104.02131v3

physics.soc-ph

th

This is an introductory textbook of the history of economics of inequality for undergraduates and genreral readers. It begins with Adam Smith's critique of Rousseau. The first and second chapters focus on Smith and Karl Marx, in the broad classical tradition of economics, where it is believed that there is an inseparable relationship between production and distribution, economic growth and inequality. Chapters 3 and 4 argue that despite the fact that the founders of the neoclassical school had shown an active interest in social issues, namely worker poverty, the issues of production and distribution became discussed separately among neoclassicals. Toward the end of the 20th century, however, there was a renewed awareness within economics of the problem of the relationship between production and distribution. The young Piketty's beginnings as an economist are set against this backdrop. Chapters 5 to 8 explain the circumstances of the restoration of classical concerns within the neoclassical framework. Then, in chapters 9 and 10, I discuss the fact that Thomas Piketty's seminal work is a new development in this "inequality renaissance," and try to gain a perspective on future trends in the debate. Mathematical appendix presents simple models of growth and distribution.

The Struggle with Inequality

2021-04-15 14:18:21

Shin-Ichiro Inaba

http://arxiv.org/abs/2104.07379v2, http://arxiv.org/pdf/2104.07379v2

econ.GN

th

A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a Best and Final Offer (BAFO) stage. This final bid can depend on new information provided about either the asset or the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information settings. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer to not reveal information.

I Want to Tell You? Maximizing Revenue in First-Price Two-Stage Auctions

2021-04-20 16:06:59

Galit Ashkenazi-Golan, Yevgeny Tsodikovich, Yannick Viossat

http://arxiv.org/abs/2104.09942v1, http://arxiv.org/pdf/2104.09942v1

cs.GT

th

Barseghyan and Molinari (2023) give sufficient conditions for semi-nonparametric point identification of parameters of interest in a mixture model of decision-making under risk, allowing for unobserved heterogeneity in utility functions and limited consideration. A key assumption in the model is that the heterogeneity of risk preferences is unobservable but context-independent. In this comment, we build on their insights and present identification results in a setting where the risk preferences are allowed to be context-dependent.

Context-Dependent Heterogeneous Preferences: A Comment on Barseghyan and Molinari (2023)

2023-05-18 15:50:58

Matias D. Cattaneo, Xinwei Ma, Yusufcan Masatlioglu

http://arxiv.org/abs/2305.10934v1, http://arxiv.org/pdf/2305.10934v1

econ.TH

th

We develop a rational inattention theory of echo chamber, whereby players gather information about an uncertain state by allocating limited attention capacities across biased primary sources and other players. The resulting Poisson attention network transmits information from the primary source to a player either directly, or indirectly through the other players. Rational inattention generates heterogeneous demands for information among players who are biased toward different decisions. In an echo chamber equilibrium, each player restricts attention to his own-biased source and like-minded friends, as the latter attend to the same primary source as his, and so could serve as secondary sources in case the information transmission from the primary source to him is disrupted. We provide sufficient conditions that give rise to echo chamber equilibria, characterize the attention networks inside echo chambers, and use our results to inform the design and regulation of information platforms.

A Rational Inattention Theory of Echo Chamber

2021-04-21 20:32:04

Lin Hu, Anqi Li, Xu Tan

http://arxiv.org/abs/2104.10657v7, http://arxiv.org/pdf/2104.10657v7

econ.TH

th

Decades of research suggest that information exchange in groups and organizations can reliably improve judgment accuracy in tasks such as financial forecasting, market research, and medical decision-making. However, we show that improving the accuracy of numeric estimates does not necessarily improve the accuracy of decisions. For binary choice judgments, also known as classification tasks--e.g. yes/no or build/buy decisions--social influence is most likely to grow the majority vote share, regardless of the accuracy of that opinion. As a result, initially inaccurate groups become increasingly inaccurate after information exchange even as they signal stronger support. We term this dynamic the "crowd classification problem." Using both a novel dataset as well as a reanalysis of three previous datasets, we study this process in two types of information exchange: (1) when people share votes only, and (2) when people form and exchange numeric estimates prior to voting. Surprisingly, when people exchange numeric estimates prior to voting, the binary choice vote can become less accurate even as the average numeric estimate becomes more accurate. Our findings recommend against voting as a form of decision-making when groups are optimizing for accuracy. For those cases where voting is required, we discuss strategies for managing communication to avoid the crowd classification problem. We close with a discussion of how our results contribute to a broader contingency theory of collective intelligence.

The Crowd Classification Problem: Social Dynamics of Binary Choice Accuracy

2021-04-22 23:00:52

Joshua Becker, Douglas Guilbeault, Ned Smith

http://arxiv.org/abs/2104.11300v1, http://arxiv.org/pdf/2104.11300v1

econ.GN

th

We modify the standard model of price competition with horizontally differentiated products, imperfect information, and search frictions by allowing consumers to flexibly acquire information about a product's match value during their visits. We characterize a consumer's optimal search and information acquisition protocol and analyze the pricing game between firms. Notably, we establish that in search markets there are fundamental differences between search frictions and information frictions, which affect market prices, profits, and consumer welfare in markedly different ways. Although higher search costs beget higher prices (and profits for firms), higher information acquisition costs lead to lower prices and may benefit consumers. We discuss implications of our findings for policies concerning disclosure rules and hidden fees.

Search and Competition with Flexible Investigations

2021-04-27 16:07:51

Vasudha Jain, Mark Whitmeyer

http://arxiv.org/abs/2104.13159v1, http://arxiv.org/pdf/2104.13159v1

econ.TH

th

Many real-world games contain parameters which can affect payoffs, action spaces, and information states. For fixed values of the parameters, the game can be solved using standard algorithms. However, in many settings agents must act without knowing the values of the parameters that will be encountered in advance. Often the decisions must be made by a human under time and resource constraints, and it is unrealistic to assume that a human can solve the game in real time. We present a new framework that enables human decision makers to make fast decisions without the aid of real-time solvers. We demonstrate applicability to a variety of situations including settings with multiple players and imperfect information.

Human strategic decision making in parametrized games

2021-04-30 06:40:27

Sam Ganzfried

http://arxiv.org/abs/2104.14744v3, http://arxiv.org/pdf/2104.14744v3

cs.GT

th

We study two-sided reputational bargaining with opportunities to issue an ultimatum -- threats to force dispute resolution. Each player is either a justified type, who never concedes and issues an ultimatum whenever an opportunity arrives, or an unjustified type, who can concede, wait, or bluff with an ultimatum. In equilibrium, the presence of ultimatum opportunities can harm or benefit a player by decelerating or accelerating reputation building. When only one player can issue an ultimatum, equilibrium play is unique. The hazard rate of dispute resolution is discontinuous and piecewise monotonic in time. As the probabilities of being justified vanish, agreement is immediate and efficient, and if the set of justifiable demands is rich, payoffs modify Abreu and Gul (2000), with the discount rate replaced by the ultimatum opportunity arrival rate if the former is smaller. When both players' ultimatum opportunities arrive sufficiently fast, there may exist multiple equilibria in which their reputations do not build up and negotiation lasts forever.

Reputational Bargaining with Ultimatum Opportunities

2021-05-04 18:44:48

Mehmet Ekmekci, Hanzhe Zhang

http://arxiv.org/abs/2105.01581v1, http://arxiv.org/pdf/2105.01581v1

econ.TH

th

The present work generalizes the analytical results of Petrikaite (2016) to a market where more than two firms interact. As a consequence, for a generic number of firms in the oligopoly model described by Janssen et al (2005), the relationship between the critical discount factor which sustains the monopoly collusive allocation and the share of perfectly informed buyers is non-monotonic, reaching a unique internal point of minimum. The first section locates the work within the proper economic framework. The second section hosts the analytical computations and the mathematical reasoning needed to derive the desired generalization, which mainly relies on the Leibniz rule for the differentiation under the integral sign and the Bounded Convergence Theorem.

Sustainability of Collusion and Market Transparency in a Sequential Search Market: a Generalization

2021-05-05 17:49:10

Jacopo De Tullio, Giuseppe Puleio

http://arxiv.org/abs/2105.02094v1, http://arxiv.org/pdf/2105.02094v1

econ.TH

th

This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful techniques in computational geometry and the literature on splines, to compute the probability density function, the cumulative distribution function, and the k-th moment of the probability function. Our algorithmic tools and implementations efficiently handle portfolios with 10000 assets, and compute moments of order k up to 40 in a few seconds, thus handling real-life scenarios. We focus on the long-only strategy which is the most common type of investment, i.e. on portfolios whose weights are non-negative and sum up to 1; our approach is readily generalizable. Thus, we leverage a geometric representation of the stock market, where the investment set defines a simplex polytope. The cumulative distribution function corresponds to a portfolio score capturing the percentage of portfolios yielding a return not exceeding a given value. We introduce closed-form analytic formulas for the first 4 moments of the cross-sectional returns distribution, as well as a novel algorithm to compute all higher moments. We show that the first 4 moments are a direct mapping of the asset returns' moments. All of our algorithms and solutions are fully general and include the special case of equal asset returns, which was sometimes excluded in previous works. Finally, we apply our portfolio score in the design of new performance measures and asset management. We found our score-based optimal portfolios less concentrated than the mean-variance portfolio and much less risky in terms of ranking.

The cross-sectional distribution of portfolio returns and applications

2021-05-14 01:29:12

Ludovic Calès, Apostolos Chalkis, Ioannis Z. Emiris

http://arxiv.org/abs/2105.06573v1, http://arxiv.org/pdf/2105.06573v1

cs.CE

th

Motivated by a variety of online matching platforms, we consider demand and supply units which are located i.i.d. in [0,1]^d, and each demand unit needs to be matched with a supply unit. The goal is to minimize the expected average distance between matched pairs (the "cost"). We model dynamic arrivals of one or both of demand and supply with uncertain locations of future arrivals, and characterize the scaling behavior of the achievable cost in terms of system size (number of supply units), as a function of the dimension d. Our achievability results are backed by concrete matching algorithms. Across cases, we find that the platform can achieve cost (nearly) as low as that achievable if the locations of future arrivals had been known beforehand. Furthermore, in all cases except one, cost nearly as low in terms of scaling as the expected distance to the nearest neighboring supply unit is achievable, i.e., the matching constraint does not cause an increase in cost either. The aberrant case is where only demand arrivals are dynamic, and d=1; excess supply significantly reduces cost in this case.

Dynamic Spatial Matching

2021-05-16 04:49:58

Yash Kanoria

http://arxiv.org/abs/2105.07329v3, http://arxiv.org/pdf/2105.07329v3

math.PR

th

We consider a generalization of rational inattention problems by measuring costs of information through the information radius (Sibson, 1969; Verd\'u, 2015) of statistical experiments. We introduce a notion of attention elasticity measuring the sensitivity of attention strategies with respect to changes in incentives. We show how the introduced class of cost functions controls attention elasticities while the Shannon model restricts attention elasticity to be unity. We explore further differences and similarities relative to the Shannon model in relation to invariance, posterior separability, consideration sets, and the ability to learn events with certainty. Lastly, we provide an efficient alternating minimization method -- analogous to the Blahut-Arimoto algorithm -- to obtain optimal attention strategies.

Attention elasticities and invariant information costs

2021-05-17 04:24:32

Dániel Csaba

http://arxiv.org/abs/2105.07565v1, http://arxiv.org/pdf/2105.07565v1

econ.GN

th

The maximin share (MMS) guarantee is a desirable fairness notion for allocating indivisible goods. While MMS allocations do not always exist, several approximation techniques have been developed to ensure that all agents receive a fraction of their maximin share. We focus on an alternative approximation notion, based on the population of agents, that seeks to guarantee MMS for a fraction of agents. We show that no optimal approximation algorithm can satisfy more than a constant number of agents, and discuss the existence and computation of MMS for all but one agent and its relation to approximate MMS guarantees. We then prove the existence of allocations that guarantee MMS for $\frac{2}{3}$ of agents, and devise a polynomial time algorithm that achieves this bound for up to nine agents. A key implication of our result is the existence of allocations that guarantee $\text{MMS}^{\lceil{3n/2}\rceil}$, i.e., the value that agents receive by partitioning the goods into $\lceil{\frac{3}{2}n}\rceil$ bundles, improving the best known guarantee of $\text{MMS}^{2n-2}$. Finally, we provide empirical experiments using synthetic data.

Guaranteeing Maximin Shares: Some Agents Left Behind

2021-05-19 23:17:42

Hadi Hosseini, Andrew Searns

http://arxiv.org/abs/2105.09383v1, http://arxiv.org/pdf/2105.09383v1

cs.GT

th

This exercise proposes a learning mechanism to model economic agent's decision-making process using an actor-critic structure in the literature of artificial intelligence. It is motivated by the psychology literature of learning through reinforcing good or bad decisions. In a model of an environment, to learn to make decisions, this AI agent needs to interact with its environment and make explorative actions. Each action in a given state brings a reward signal to the agent. These interactive experience is saved in the agent's memory, which is then used to update its subjective belief of the world. The agent's decision-making strategy is formed and adjusted based on this evolving subjective belief. This agent does not only take an action that it knows would bring a high reward, it also explores other possibilities. This is the process of taking explorative actions, and it ensures that the agent notices changes in its environment and adapt its subjective belief and decisions accordingly. Through a model of stochastic optimal growth, I illustrate that the economic agent under this proposed learning structure is adaptive to changes in an underlying stochastic process of the economy. AI agents can differ in their levels of exploration, which leads to different experience in the same environment. This reflects on to their different learning behaviours and welfare obtained. The chosen economic structure possesses the fundamental decision making problems of macroeconomic models, i.e., how to make consumption-saving decisions in a lifetime, and it can be generalised to other decision-making processes and economic models.

Learning from zero: how to make consumption-saving decisions in a stochastic environment with an AI algorithm

2021-05-21 05:39:12

Rui, Shi

http://arxiv.org/abs/2105.10099v2, http://arxiv.org/pdf/2105.10099v2

econ.TH

th

This paper introduces Gm, which is a category for extensive-form games. It also provides some applications. The category's objects are games, which are understood to be sets of nodes which have been endowed with edges, information sets, actions, players, and utility functions. Its arrows are functions from source nodes to target nodes that preserve the additional structure. For instance, a game's information-set collection is newly regarded as a topological basis for the game's decision-node set, and thus a morphism's continuity serves to preserve information sets. Given these definitions, a game monomorphism is characterized by the property of not mapping two source runs (plays) to the same target run. Further, a game isomorphism is characterized as a bijection whose restriction to decision nodes is a homeomorphism, whose induced player transformation is injective, and which strictly preserves the ordinal content of the utility functions. The category is then applied to some game-theoretic concepts beyond the definition of a game. A Selten subgame is characterized as a special kind of categorical subgame, and game isomorphisms are shown to preserve strategy sets, Nash equilibria, Selten subgames, subgame-perfect equilibria, perfect-information, and no-absentmindedness. Further, it is shown that the full subcategory for distinguished-action sequence games is essentially wide in the category of all games, and that the full subcategory of action-set games is essentially wide in the full subcategory for games with no-absentmindedness.

A Category for Extensive-Form Games

2021-05-24 19:40:42

Peter A. Streufert

http://arxiv.org/abs/2105.11398v1, http://arxiv.org/pdf/2105.11398v1

econ.TH

th

A monopolist seller of multiple goods screens a buyer whose type is initially unknown to both but drawn from a commonly known distribution. The buyer privately learns about his type via a signal. We derive the seller's optimal mechanism in two different information environments. We begin by deriving the buyer-optimal outcome. Here, an information designer first selects a signal, and then the seller chooses an optimal mechanism in response; the designer's objective is to maximize consumer surplus. Then, we derive the optimal informationally robust mechanism. In this case, the seller first chooses the mechanism, and then nature picks the signal that minimizes the seller's profits. We derive the relation between both problems and show that the optimal mechanism in both cases takes the form of pure bundling.

Multi-Dimensional Screening: Buyer-Optimal Learning and Informational Robustness

2021-05-26 05:31:57

Rahul Deb, Anne-Katrin Roesler

http://arxiv.org/abs/2105.12304v1, http://arxiv.org/pdf/2105.12304v1

econ.TH

th

This paper studies how violations of structural assumptions like expected utility and exponential discounting can be connected to basic rationality violations caused by reference-dependent preferences, even if these assumptions are typically regarded as independent building blocks of decision theory. A reference-dependent generalization of behavioral postulates captures preference changes across various choice domains. It gives rise to a linear order that endogenously determines reference alternatives, which in turn determines the preference parameters for a choice problem. With canonical models as foundation, preference changes are captured using known technologies like the concavity of utility functions and the levels of discount factors. The framework allows us to study risk, time, and social preferences collectively, where seemingly independent anomalies are interconnected through the lens of reference-dependent choice.

Ordered Reference Dependent Choice

2021-05-27 05:22:02

Xi Zhi Lim

http://arxiv.org/abs/2105.12915v4, http://arxiv.org/pdf/2105.12915v4

econ.TH

th

We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical revealed preference axioms, as well as generate new axioms for behavioral theories, and show that a data set is rationalizable if and only if it is consistent with an algebraic axiom.

An algebraic approach to revealed preferences

2021-05-31 20:34:06

Mikhail Freer, Cesar Martinelli

http://arxiv.org/abs/2105.15175v1, http://arxiv.org/pdf/2105.15175v1

econ.TH

th

We consider the algorithmic question of choosing a subset of candidates of a given size $k$ from a set of $m$ candidates, with knowledge of voters' ordinal rankings over all candidates. We consider the well-known and classic scoring rule for achieving diverse representation: the Chamberlin-Courant (CC) or $1$-Borda rule, where the score of a committee is the average over the voters, of the rank of the best candidate in the committee for that voter; and its generalization to the average of the top $s$ best candidates, called the $s$-Borda rule. Our first result is an improved analysis of the natural and well-studied greedy heuristic. We show that greedy achieves a $\left(1 - \frac{2}{k+1}\right)$-approximation to the maximization (or satisfaction) version of CC rule, and a $\left(1 - \frac{2s}{k+1}\right)$-approximation to the $s$-Borda score. Our result improves on the best known approximation algorithm for this problem. We show that these bounds are almost tight. For the dissatisfaction (or minimization) version of the problem, we show that the score of $\frac{m+1}{k+1}$ can be viewed as an optimal benchmark for the CC rule, as it is essentially the best achievable score of any polynomial-time algorithm even when the optimal score is a polynomial factor smaller (under standard computational complexity assumptions). We show that another well-studied algorithm for this problem, called the Banzhaf rule, attains this benchmark. We finally show that for the $s$-Borda rule, when the optimal value is small, these algorithms can be improved by a factor of $\tilde \Omega(\sqrt{s})$ via LP rounding. Our upper and lower bounds are a significant improvement over previous results, and taken together, not only enable us to perform a finer comparison of greedy algorithms for these problems, but also provide analytic justification for using such algorithms in practice.

Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule

2021-05-31 23:28:59

Kamesh Munagala, Zeyu Shen, Kangning Wang

http://dx.doi.org/10.1145/3465456.3467624, http://arxiv.org/abs/2106.00091v1, http://arxiv.org/pdf/2106.00091v1

cs.GT

th

The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in Lagrangian mechanics. In the differential-algebraic equation framework of General Constrained Dynamics (GCD), households, firms, banks, and the government employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The flexible out-of-equilibrium model can combine Keynesian concepts such as the balance sheet approach and slow adaptation of prices and quantities with bounded rationality (gradient climbing) and interacting agents discussed in behavioral economics and agent-based models. The framework integrates some elements of different schools of thought and overcomes some restrictions inherent to optimization approaches, such as the assumption of markets operating in or close to equilibrium. Depending on the parameter choice for power relations and adaptation speeds, the model nevertheless can converge to a neoclassical equilibrium, and reacts to an austerity shock in a neoclassical or post-Keynesian way.

Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints

2021-06-01 16:39:37

Oliver Richters

http://dx.doi.org/10.1016/j.jebo.2021.06.005, http://arxiv.org/abs/2106.00483v2, http://arxiv.org/pdf/2106.00483v2

econ.TH

th

We initiate the work towards a comprehensive picture of the smoothed satisfaction of voting axioms, to provide a finer and more realistic foundation for comparing voting rules. We adopt the smoothed social choice framework, where an adversary chooses arbitrarily correlated "ground truth" preferences for the agents, on top of which random noises are added. We focus on characterizing the smoothed satisfaction of two well-studied voting axioms: Condorcet criterion and participation. We prove that for any fixed number of alternatives, when the number of voters $n$ is sufficiently large, the smoothed satisfaction of the Condorcet criterion under a wide range of voting rules is $1$, $1-\exp(-\Theta(n))$, $\Theta(n^{-0.5})$, $ \exp(-\Theta(n))$, or being $\Theta(1)$ and $1-\Theta(1)$ at the same time; and the smoothed satisfaction of participation is $1-\Theta(n^{-0.5})$. Our results address open questions by Berg and Lepelley in 1994 for these rules, and also confirm the following high-level message: the Condorcet criterion is a bigger concern than participation under realistic models.

The Smoothed Satisfaction of Voting Axioms

2021-06-03 18:55:11

Lirong Xia

http://arxiv.org/abs/2106.01947v1, http://arxiv.org/pdf/2106.01947v1

econ.TH

th

A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time $T$, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms. I.e., mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer's value distribution.

Optimal Pricing Schemes for an Impatient Buyer

2021-06-04 00:53:37

Yuan Deng, Jieming Mao, Balasubramanian Sivan, Kangning Wang

http://dx.doi.org/10.1137/1.9781611977554.ch16, http://arxiv.org/abs/2106.02149v2, http://arxiv.org/pdf/2106.02149v2

cs.GT

th

All economies require physical resource consumption to grow and maintain their structure. The modern economy is additionally characterized by private debt. The Human and Resources with MONEY (HARMONEY) economic growth model links these features using a stock and flow consistent framework in physical and monetary units. Via an updated version, we explore the interdependence of growth and three major structural metrics of an economy. First, we show that relative decoupling of gross domestic product (GDP) from resource consumption is an expected pattern that occurs because of physical limits to growth, not a response to avoid physical limits. While an increase in resource efficiency of operating capital does increase the level of relative decoupling, so does a change in pricing from one based on full costs to one based only on marginal costs that neglects depreciation and interest payments leading to higher debt ratios. Second, if assuming full labor bargaining power for wages, when a previously-growing economy reaches peak resource extraction and GDP, wages remain high but profits and debt decline to zero. By removing bargaining power, profits can remain positive at the expense of declining wages. Third, the distribution of intermediate transactions within the input-output table of the model follows the same temporal pattern as in the post-World War II U.S. economy. These results indicate that the HARMONEY framework enables realistic investigation of interdependent structural change and trade-offs between economic distribution, size, and resources consumption.

Interdependence of Growth, Structure, Size and Resource Consumption During an Economic Growth Cycle

2021-06-04 17:29:50

Carey W. King

http://arxiv.org/abs/2106.02512v1, http://arxiv.org/pdf/2106.02512v1

econ.TH

th

The optimal taxation of assets requires attention to two concerns: 1) the elasticity of the supply of assets and 2) the impact of taxing assets on distributional objectives. The most efficient way to attend to these two concerns is to tax assets of different types separately, rather than having one tax on all assets. When assets are created by specialized effort rather than by saving, as with innovations, discoveries of mineral deposits and development of unregulated natural monopolies, it is interesting to consider a regime in which the government awards a prize for the creation of the asset and then collects the remaining value of the asset in taxes. Analytically, the prize is like a wage after taxes. In this perspective, prizes are awarded based on a variation on optimal taxation theory, while assets of different types are taxed in divergent ways, depending on their characteristics. Some categories of assets are abolished.

Optimal Taxation of Assets

2021-06-05 13:27:19

Nicolaus Tideman, Thomas Mecherikunnel

http://arxiv.org/abs/2106.02861v1, http://arxiv.org/pdf/2106.02861v1

econ.GN

th

This paper studies a multi-armed bandit problem where the decision-maker is loss averse, in particular she is risk averse in the domain of gains and risk loving in the domain of losses. The focus is on large horizons. Consequences of loss aversion for asymptotic (large horizon) properties are derived in a number of analytical results. The analysis is based on a new central limit theorem for a set of measures under which conditional variances can vary in a largely unstructured history-dependent way subject only to the restriction that they lie in a fixed interval.

A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

2021-06-10 06:15:11

Zengjing Chen, Larry G. Epstein, Guodong Zhang

http://arxiv.org/abs/2106.05472v2, http://arxiv.org/pdf/2106.05472v2

math.PR

th

The spread of disinformation on social platforms is harmful to society. This harm may manifest as a gradual degradation of public discourse; but it can also take the form of sudden dramatic events such as the 2021 insurrection on Capitol Hill. The platforms themselves are in the best position to prevent the spread of disinformation, as they have the best access to relevant data and the expertise to use it. However, mitigating disinformation is costly, not only for implementing detection algorithms or employing manual effort, but also because limiting such highly viral content impacts user engagement and potential advertising revenue. Since the costs of harmful content are borne by other entities, the platform will therefore have no incentive to exercise the socially-optimal level of effort. This problem is similar to that of environmental regulation, in which the costs of adverse events are not directly borne by a firm, the mitigation effort of a firm is not observable, and the causal link between a harmful consequence and a specific failure is difficult to prove. For environmental regulation, one solution is to perform costly monitoring to ensure that the firm takes adequate precautions according to a specified rule. However, a fixed rule for classifying disinformation becomes less effective over time, as bad actors can learn to sequentially and strategically bypass it. Encoding our domain as a Markov decision process, we demonstrate that no penalty based on a static rule, no matter how large, can incentivize optimal effort. Penalties based on an adaptive rule can incentivize optimal effort, but counter-intuitively, only if the regulator sufficiently overreacts to harmful events by requiring a greater-than-optimal level of effort. We offer novel insights for the effective regulation of social platforms, highlight inherent challenges, and discuss promising avenues for future work.

Disinformation, Stochastic Harm, and Costly Effort: A Principal-Agent Analysis of Regulating Social Media Platforms

2021-06-18 02:27:43

Shehroze Khan, James R. Wright

http://arxiv.org/abs/2106.09847v5, http://arxiv.org/pdf/2106.09847v5

cs.GT

th

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected.

Measuring Violations of Positive Involvement in Voting

2021-06-22 05:46:37

Wesley H. Holliday, Eric Pacuit

http://dx.doi.org/10.4204/EPTCS.335.17, http://arxiv.org/abs/2106.11502v1, http://arxiv.org/pdf/2106.11502v1

cs.GT

th

When reasoning about strategic behavior in a machine learning context it is tempting to combine standard microfoundations of rational agents with the statistical decision theory underlying classification. In this work, we argue that a direct combination of these standard ingredients leads to brittle solution concepts of limited descriptive and prescriptive value. First, we show that rational agents with perfect information produce discontinuities in the aggregate response to a decision rule that we often do not observe empirically. Second, when any positive fraction of agents is not perfectly strategic, desirable stable points -- where the classifier is optimal for the data it entails -- cease to exist. Third, optimal decision rules under standard microfoundations maximize a measure of negative externality known as social burden within a broad class of possible assumptions about agent behavior. Recognizing these limitations we explore alternatives to standard microfoundations for binary classification. We start by describing a set of desiderata that help navigate the space of possible assumptions about how agents respond to a decision rule. In particular, we analyze a natural constraint on feature manipulations, and discuss properties that are sufficient to guarantee the robust existence of stable points. Building on these insights, we then propose the noisy response model. Inspired by smoothed analysis and empirical observations, noisy response incorporates imperfection in the agent responses, which we show mitigates the limitations of standard microfoundations. Our model retains analytical tractability, leads to more robust insights about stable points, and imposes a lower social burden at optimality.

Alternative Microfoundations for Strategic Classification

2021-06-24 03:30:58

Meena Jagadeesan, Celestine Mendler-Dünner, Moritz Hardt

http://arxiv.org/abs/2106.12705v1, http://arxiv.org/pdf/2106.12705v1

cs.LG

th

This paper unifies two key results from economic theory, namely, revealed rational inattention and classical revealed preference. Revealed rational inattention tests for rationality of information acquisition for Bayesian decision makers. On the other hand, classical revealed preference tests for utility maximization under known budget constraints. Our first result is an equivalence result - we unify revealed rational inattention and revealed preference through an equivalence map over decision parameters and partial order for payoff monotonicity over the decision space in both setups. Second, we exploit the unification result computationally to extend robustness measures for goodness-of-fit of revealed preference tests in the literature to revealed rational inattention. This extension facilitates quantifying how well a Bayesian decision maker's actions satisfy rational inattention. Finally, we illustrate the significance of the unification result on a real-world YouTube dataset comprising thumbnail, title and user engagement metadata from approximately 140,000 videos. We compute the Bayesian analog of robustness measures from revealed preference literature on YouTube metadata features extracted from a deep auto-encoder, i.e., a deep neural network that learns low-dimensional features of the metadata. The computed robustness values show that YouTube user engagement fits the rational inattention model remarkably well. All our numerical experiments are completely reproducible.

Unifying Revealed Preference and Revealed Rational Inattention

2021-06-28 12:01:09

Kunal Pattanayak, Vikram Krishnamurthy

http://arxiv.org/abs/2106.14486v4, http://arxiv.org/pdf/2106.14486v4

econ.TH

th

The intermittent nature of renewable energy resources creates extra challenges in the operation and control of the electricity grid. Demand flexibility markets can help in dealing with these challenges by introducing incentives for customers to modify their demand. Market-based demand-side management (DSM) have garnered serious attention lately due to its promising capability of maintaining the balance between supply and demand, while also keeping customer satisfaction at its highest levels. Many researchers have proposed using concepts from mechanism design theory in their approaches to market-based DSM. In this work, we provide a review of the advances in market-based DSM using mechanism design. We provide a categorisation of the reviewed literature and evaluate the strengths and weaknesses of each design criteria. We also study the utility function formulations used in the reviewed literature and provide a critique of the proposed indirect mechanisms. We show that despite the extensiveness of the literature on this subject, there remains concerns and challenges that should be addressed for the realistic implementation of such DSM approaches. We draw conclusions from our review and discuss possible future research directions.

Applications of Mechanism Design in Market-Based Demand-Side Management

2021-06-24 14:24:41

Khaled Abedrabboh, Luluwah Al-Fagih

http://arxiv.org/abs/2106.14659v1, http://arxiv.org/pdf/2106.14659v1

cs.GT

th

This paper attempts to analyse policymaking in the field of Intellectual Property (IP) as an instrument of economic growth across the Global North and South. It begins by studying the links between economic growth and IP, followed by an understanding of Intellectual Property Rights (IPR) development in the US, a leading proponent of robust IPR protection internationally. The next section compares the IPR in the Global North and South and undertakes an analysis of the diverse factors that result in these differences. The paper uses the case study of the Indian Pharmaceutical Industry to understand how IPR may differentially affect economies and conclude that there may not yet be a one size fits all policy for the adoption of Intellectual Property Rights.

Comparing Intellectual property policy in the Global North and South -- A one-size-fits-all policy for economic prosperity?

2021-07-14 20:20:43

S Sidhartha Narayan, Malavika Ranjan, Madhumitha Raghuraman

http://arxiv.org/abs/2107.06855v2, http://arxiv.org/pdf/2107.06855v2

econ.TH

th

Lloyd S. Shapley \cite{Shapley1953a, Shapley1953} introduced a set of axioms in 1953, now called the {\em Shapley axioms}, and showed that the axioms characterize a natural allocation among the players who are in grand coalition of a {\em cooperative game}. Recently, \citet{StTe2019} showed that a cooperative game can be decomposed into a sum of {\em component games}, one for each player, whose value at the grand coalition coincides with the {\em Shapley value}. The component games are defined by the solutions to the naturally defined system of least squares linear equations via the framework of the {\em Hodge decomposition} on the hypercube graph. In this paper we propose a new set of axioms which characterizes the component games. Furthermore, we realize them through an intriguing stochastic path integral driven by a canonical Markov chain. The integrals are natural representation for the expected total contribution made by the players for each coalition, and hence can be viewed as their fair share. This allows us to interpret the component game values for each coalition also as a valid measure of fair allocation among the players in the coalition. Our axioms may be viewed as a completion of Shapley axioms in view of this characterization of the Hodge-theoretic component games, and moreover, the stochastic path integral representation of the component games may be viewed as an extension of the {\em Shapley formula}.

A Hodge theoretic extension of Shapley axioms

2021-06-29 08:11:02

Tongseok Lim

http://arxiv.org/abs/2106.15094v3, http://arxiv.org/pdf/2106.15094v3

math.OC

th

The matching literature often recommends market centralization under the assumption that agents know their own preferences and that their preferences are fixed. We find counterevidence to this assumption in a quasi-experiment. In Germany's university admissions, a clearinghouse implements the early stages of the Gale-Shapley algorithm in real time. We show that early offers made in this decentralized phase, although not more desirable, are accepted more often than later ones. These results, together with survey evidence and a theoretical model, are consistent with students' costly learning about universities. We propose a hybrid mechanism to combine the advantages of decentralization and centralization. Published at The Journal of Political Economy under a new title, ``Preference Discovery in University Admissions: The Case for Dynamic Multioffer Mechanisms,'' available at https://doi.org/10.1086/718983 (Open Access).

Decentralizing Centralized Matching Markets: Implications from Early Offers in University Admissions

2021-07-04 06:37:19

Julien Grenet, YingHua He, Dorothea Kübler

http://dx.doi.org/10.1086/718983, http://arxiv.org/abs/2107.01532v2, http://arxiv.org/pdf/2107.01532v2

econ.GN

th

We propose a model, which nests a susceptible-infected-recovered-deceased (SIRD) epidemic model into a dynamic macroeconomic equilibrium framework with agents' mobility. The latter affect both their income and their probability of infecting and being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. The continuum of rational forward-looking agents coordinates on the Nash equilibrium of a discrete time, finite-state, infinite-horizon Mean Field Game. We prove the existence of an equilibrium and provide a recursive construction method for the search of an equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic and we discuss policy implications.

Mobility decisions, economic dynamics and epidemic

2021-07-05 01:54:40

Giorgio Fabbri, Salvatore Federico, Davide Fiaschi, Fausto Gozzi

http://dx.doi.org/10.1007/s00199-023-01485-1, http://arxiv.org/abs/2107.01746v2, http://arxiv.org/pdf/2107.01746v2

econ.GN

th

Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven by the desire to use the blockchain itself as a source of pseudorandomness \cite{brown2019formal}. We consider instead a longest-chain Proof-of-Stake protocol with perfect, trusted, external randomness (e.g. a randomness beacon). We produce two main results. First, we show that a strategic miner can strictly outperform an honest miner with just $32.5\%$ of the total stake. Note that a miner of this size {\em cannot} outperform an honest miner in the Proof-of-Work model. This establishes that even with access to a perfect randomness beacon, incentives in Proof-of-Work and Proof-of-Stake longest-chain protocols are fundamentally different. Second, we prove that a strategic miner cannot outperform an honest miner with $30.8\%$ of the total stake. This means that, while not quite as secure as the Proof-of-Work regime, desirable incentive properties of Proof-of-Work longest-chain protocols can be approximately recovered via Proof-of-Stake with a perfect randomness beacon. The space of possible strategies in a Proof-of-Stake mining game is {\em significantly} richer than in a Proof-of-Work game. Our main technical contribution is a characterization of potentially optimal strategies for a strategic miner, and in particular, a proof that the corresponding infinite-state MDP admits an optimal strategy that is positive recurrent.

Proof-of-Stake Mining Games with Perfect Randomness

2021-07-08 22:01:58

Matheus V. X. Ferreira, S. Matthew Weinberg

http://dx.doi.org/10.1145/3465456.3467636, http://arxiv.org/abs/2107.04069v2, http://arxiv.org/pdf/2107.04069v2

cs.GT

th

We study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used Deferred Acceptance mechanism (Gale and Shapley, 1962). We show that many complete-information results are fragile to a small infusion of uncertainty about others' preferences.

Centralized Matching with Incomplete Information

2021-07-08 23:32:22

Marcelo Ariel Fernandez, Kirill Rudov, Leeat Yariv

http://arxiv.org/abs/2107.04098v1, http://arxiv.org/pdf/2107.04098v1

econ.TH

th

The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (Par), half-way monotonicity (HM), Maskin monotonicity (MM), and strategy-proofness (SP). Such incompatibilities are often known as impossibility theorems, and are proved by worst-case analysis. Previous work has investigated the likelihood for these impossibilities to occur under certain models, which are often criticized of being unrealistic. We strengthen previous work by proving the first set of semi-random impossibilities for voting rules to satisfy CC and the more general, group versions of the four desiderata: for any sufficiently large number of voters $n$, any size of the group $1\le B\le \sqrt n$, any voting rule $r$, and under a large class of {\em semi-random} models that include Impartial Culture, the likelihood for $r$ to satisfy CC and Par, CC and HM, CC and MM, or CC and SP is $1-\Omega(\frac{B}{\sqrt n})$. This matches existing lower bounds for CC and Par ($B=1$) and CC and SP ($B\le \sqrt n$), showing that many commonly-studied voting rules are already asymptotically optimal in such cases.

Semi-Random Impossibilities of Condorcet Criterion

2021-07-14 03:39:33

Lirong Xia

http://arxiv.org/abs/2107.06435v2, http://arxiv.org/pdf/2107.06435v2

econ.TH

th

With the growing use of distributed machine learning techniques, there is a growing need for data markets that allows agents to share data with each other. Nevertheless data has unique features that separates it from other commodities including replicability, cost of sharing, and ability to distort. We study a setup where each agent can be both buyer and seller of data. For this setup, we consider two cases: bilateral data exchange (trading data with data) and unilateral data exchange (trading data with money). We model bilateral sharing as a network formation game and show the existence of strongly stable outcome under the top agents property by allowing limited complementarity. We propose ordered match algorithm which can find the stable outcome in O(N^2) (N is the number of agents). For the unilateral sharing, under the assumption of additive cost structure, we construct competitive prices that can implement any social welfare maximizing outcome. Finally for this setup when agents have private information, we propose mixed-VCG mechanism which uses zero cost data distortion of data sharing with its isolated impact to achieve budget balance while truthfully implementing socially optimal outcomes to the exact level of budget imbalance of standard VCG mechanisms. Mixed-VCG uses data distortions as data money for this purpose. We further relax zero cost data distortion assumption by proposing distorted-mixed-VCG. We also extend our model and results to data sharing via incremental inquiries and differential privacy costs.

Data Sharing Markets

2021-07-19 09:00:34

Mohammad Rasouli, Michael I. Jordan

http://arxiv.org/abs/2107.08630v2, http://arxiv.org/pdf/2107.08630v2

econ.TH

th

In economy, viewed as a quantum system working as a circuit, each process at the microscale is a quantum gate among agents. The global configuration of economy is addressed by optimizing the sustainability of the whole circuit. This is done in terms of geodesics, starting from some approximations. A similar yet somehow different approach is applied for the closed system of the whole and for economy as an open system. Computations may partly be explicit, especially when the reality is represented in a simplified way. The circuit can be also optimized by minimizing its complexity, with a partly similar formalism, yet generally not along the same paths.

Sustainability of Global Economy as a Quantum Circuit

2021-07-13 11:40:47

Antonino Claudio Bonan

http://arxiv.org/abs/2107.09032v1, http://arxiv.org/pdf/2107.09032v1

econ.TH

th

This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and Hodge-theoretic discrete Poisson's equations on general weighted graphs. More precisely, we begin by defining cooperative games on general graphs and generalize Shapley's value allocation formula for those games in terms of stochastic path integral driven by the associated canonical Markov chain. We then show the value allocation operator, one for each player defined by the path integral, turns out to be the solution to the Poisson's equation defined via the combinatorial Hodge decomposition on general weighted graphs. Several motivational examples and applications are presented, in particular, a section is devoted to reinterpret and extend Nash's and Kohlberg and Neyman's solution concept for cooperative games. This and other examples, e.g. on revenue management, suggest that our general framework does not have to be restricted to cooperative games setup, but may apply to broader range of problems arising in economics, finance and other social and physical sciences.

Hodge theoretic reward allocation for generalized cooperative games on graphs

2021-07-22 11:13:11

Tongseok Lim

http://arxiv.org/abs/2107.10510v3, http://arxiv.org/pdf/2107.10510v3

math.PR

th

This paper specifies an extensive form as a 5-ary relation (that is, as a set of quintuples) which satisfies eight abstract axioms. Each quintuple is understood to list a player, a situation (a concept which generalizes an information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a "pentaform". A "pentaform game" is then defined to be a pentaform together with utility functions. The paper's main result is to construct an intuitive bijection between pentaform games and $\mathbf{Gm}$ games (Streufert 2021, arXiv:2105.11398), which are centrally located in the literature, and which encompass all finite-horizon or infinite-horizon discrete games. In this sense, pentaform games equivalently formulate almost all extensive-form games. Secondary results concern disaggregating pentaforms by subsets, constructing pentaforms by unions, and initial applications to Selten subgames and perfect-recall (an extensive application to dynamic programming is in Streufert 2023, arXiv:2302.03855).

Specifying a Game-Theoretic Extensive Form as an Abstract 5-ary Relation

2021-07-22 19:56:07

Peter A. Streufert

http://arxiv.org/abs/2107.10801v4, http://arxiv.org/pdf/2107.10801v4

econ.TH

th

We study a model in which before a conflict between two parties escalates into a war (in the form of an all-pay auction), a party can offer a take-it-or-leave-it bribe to the other for a peaceful settlement. In contrast to the received literature, we find that peace security is impossible in our model. We characterize the necessary and sufficient conditions for peace implementability. Furthermore, we find that separating equilibria do not exist and the number of (on-path) bribes in any non-peaceful equilibria is at most two. We also consider a requesting model and characterize the necessary and sufficient conditions for the existence of robust peaceful equilibria, all of which are sustained by the identical (on-path) request. Contrary to the bribing model, peace security is possible in the requesting model.

Peace through bribing

2021-07-24 13:12:10

Jingfeng Lu, Zongwei Lu, Christian Riis

http://arxiv.org/abs/2107.11575v3, http://arxiv.org/pdf/2107.11575v3

econ.TH

th

We propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head majority comparison, then A should still win in the election with B included (unless there is another candidate A' who has the same kind of claim to winning, in which case a tiebreaker may choose between such candidates). We call this principle Stability for Winners (with Tiebreaking). Stable Voting satisfies this principle while also having a remarkable ability to avoid tied outcomes in elections even with small numbers of voters.

Stable Voting

2021-08-02 00:06:56

Wesley H. Holliday, Eric Pacuit

http://arxiv.org/abs/2108.00542v9, http://arxiv.org/pdf/2108.00542v9

econ.TH

th

Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move followed by a double move of White and then alternating play, play is more balanced because White does not always tie or lead in moves. Symbolically, Balanced Alternation gives the following move sequence: After White's (W) initial move, first Black (B) and then White each have two moves in a row (BBWW), followed by the alternating sequence, beginning with W, which altogether can be written as WB/BW/WB/WB/WB... (the slashes separate alternating pairs of moves). Except for reversal of the 3rd and 4th moves from WB to BW, this is the standard chess sequence. Because Balanced Alternation lies between the standard sequence, which favors White, and a comparable sequence that favors Black, it is highly likely to produce a draw with optimal play, rendering chess fairer. This conclusion is supported by a computer analysis of chess openings and how they would play out under Balanced Alternation.

Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black

2021-08-05 15:14:36

Steven J. Brams, Mehmet S. Ismail

http://arxiv.org/abs/2108.02547v2, http://arxiv.org/pdf/2108.02547v2

econ.TH

th

To protect his teaching evaluations, an economics professor uses the following exam curve: if the class average falls below a known target, $m$, then all students will receive an equal number of free points so as to bring the mean up to $m$. If the average is above $m$ then there is no curve; curved grades above $100\%$ will never be truncated to $100\%$ in the gradebook. The $n$ students in the course all have Cobb-Douglas preferences over the grade-leisure plane; effort corresponds exactly to earned (uncurved) grades in a $1:1$ fashion. The elasticity of each student's utility with respect to his grade is his ability parameter, or relative preference for a high score. I find, classify, and give complete formulas for all the pure Nash equilibria of my own game, which my students have been playing for some eight semesters. The game is supermodular, featuring strategic complementarities, negative spillovers, and nonsmooth payoffs that generate non-convexities in the reaction correspondence. The $n+2$ types of equilibria are totally ordered with respect to effort and Pareto preference, and the lowest $n+1$ of these types are totally ordered in grade-leisure space. In addition to the no-curve ("try-hard") and curved interior equilibria, we have the "$k$-don't care" equilibria, whereby the $k$ lowest-ability students are no-shows. As the class size becomes infinite in the curved interior equilibrium, all students increase their leisure time by a fixed percentage, i.e., $14\%$, in response to the disincentive, which amplifies any pre-existing ability differences. All students' grades inflate by this same (endogenous) factor, say, $1.14$ times what they would have been under the correct standard.

Grade Inflation and Stunted Effort in a Curved Economics Course

2021-08-08 21:48:31

Alex Garivaltis

http://arxiv.org/abs/2108.03709v3, http://arxiv.org/pdf/2108.03709v3

econ.TH

th

We propose and investigate a model for mate searching and marriage in large societies based on a stochastic matching process and simple decision rules. Agents have preferences among themselves given by some probability distribution. They randomly search for better mates, forming new couples and breaking apart in the process. Marriage is implemented in the model by adding the decision of stopping searching for a better mate when the affinity between a couple is higher than a certain fixed amount. We show that the average utility in the system with marriage can be higher than in the system without it. Part of our results can be summarized in what sounds like a piece of advice: don't marry the first person you like and don't search for the love of your life, but get married if you like your partner more than a sigma above average. We also find that the average utility attained in our stochastic model is smaller than the one associated with a stable matching achieved using the Gale-Shapley algorithm. This can be taken as a formal argument in favor of a central planner (perhaps an app) with the information to coordinate the marriage market in order to set a stable matching. To roughly test the adequacy of our model to describe existent societies, we compare the evolution of the fraction of married couples in our model with real-world data and obtain good agreement. In the last section, we formulate the model in the limit of an infinite number of agents and find an analytical expression for the evolution of the system.

Benefits of marriage as a search strategy

2021-08-10 22:24:38

Davi B. Costa

http://arxiv.org/abs/2108.04885v2, http://arxiv.org/pdf/2108.04885v2

econ.TH

th

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

Expected Values for Variable Network Games

2021-08-16 15:35:40

Subhadip Chakrabarti, Loyimee Gogoi, Robert P Gilles, Surajit Borkotokey, Rajnish Kumar

http://arxiv.org/abs/2108.07047v2, http://arxiv.org/pdf/2108.07047v2

cs.GT

th

This paper studies dynamic monopoly pricing for a class of settings that includes multiple durable, multiple rental, or a mix of varieties. We show that the driving force behind pricing dynamics is the seller's incentive to switch consumers - buyers and non-buyers - to higher-valued consumption options by lowering prices ("trading up"). If consumers cannot be traded up from the static optimal allocation, pricing dynamics do not emerge in equilibrium. If consumers can be traded up, pricing dynamics arise until all trading-up opportunities are exhausted. We study the conditions under which pricing dynamics end in finite time and characterize the final prices at which dynamics end.

Dynamic Monopoly Pricing With Multiple Varieties: Trading Up

2021-08-16 18:22:25

Stefan Buehler, Nicolas Eschenbaum

http://arxiv.org/abs/2108.07146v2, http://arxiv.org/pdf/2108.07146v2

econ.GN

th

An important but understudied question in economics is how people choose when facing uncertainty in the timing of events. Here we study preferences over time lotteries, in which the payment amount is certain but the payment time is uncertain. Expected discounted utility theory (EDUT) predicts decision makers to be risk-seeking over time lotteries. We explore a normative model of growth-optimality, in which decision makers maximise the long-term growth rate of their wealth. Revisiting experimental evidence on time lotteries, we find that growth-optimality accords better with the evidence than EDUT. We outline future experiments to scrutinise further the plausibility of growth-optimality.

Risk Preferences in Time Lotteries

2021-08-18 22:46:55

Yonatan Berman, Mark Kirstein

http://arxiv.org/abs/2108.08366v1, http://arxiv.org/pdf/2108.08366v1

econ.TH

th

It is believed that interventions that change the media's costs of misreporting can increase the information provided by media outlets. This paper analyzes the validity of this claim and the welfare implications of those types of interventions that affect misreporting costs. I study a model of communication between an uninformed voter and a media outlet that knows the quality of two competing candidates. The alternatives available to the voter are endogenously championed by the two candidates. I show that higher costs may lead to more misreporting and persuasion, whereas low costs result in full revelation; interventions that increase misreporting costs never harm the voter, but those that do so slightly may be wasteful of public resources. I conclude that intuitions derived from the interaction between the media and voters, without incorporating the candidates' strategic responses to the media environment, do not capture properly the effects of these types of interventions.

Influential News and Policy-making

2021-08-25 14:00:38

Federico Vaccari

http://arxiv.org/abs/2108.11177v1, http://arxiv.org/pdf/2108.11177v1

econ.GN

th

This paper presents six theorems and ten propositions that can be read as deconstructing and integrating the continuity postulate under the rubric of pioneering work of Eilenberg, Wold, von Neumann-Morgenstern, Herstein-Milnor and Debreu. Its point of departure is the fact that the adjective continuous applied to a function or a binary relation does not acknowledge the many meanings that can be given to the concept it names, and that under a variety of technical mathematical structures, its many meanings can be whittled down to novel and unexpected equivalences that have been missed in the theory of choice. Specifically, it provides a systematic investigation of the two-way relation between restricted and full continuity of a function and a binary relation that, under convex, monotonic and differentiable structures, draws out the behavioral implications of the postulate.

The Continuity Postulate in Economic Theory: A Deconstruction and an Integration

2021-08-26 15:29:46

Metin Uyanik, M. Ali Khan

http://arxiv.org/abs/2108.11736v2, http://arxiv.org/pdf/2108.11736v2

econ.TH

th

This paper studies the design of mechanisms that are robust to misspecification. We introduce a novel notion of robustness that connects a variety of disparate approaches and study its implications in a wide class of mechanism design problems. This notion is quantifiable, allowing us to formalize and answer comparative statics questions relating the nature and degree of misspecification to sharp predictions regarding features of feasible mechanisms. This notion also has a behavioral foundation which reflects the perception of ambiguity, thus allowing the degree of misspecification to emerge endogenously. In a number of standard settings, robustness to arbitrarily small amounts of misspecification generates a discontinuity in the set of feasible mechanisms and uniquely selects simple, ex post incentive compatible mechanisms such as second-price auctions. Robustness also sheds light on the value of private information and the prevalence of full or virtual surplus extraction.

Uncertainty in Mechanism Design

2021-08-28 14:58:45

Giuseppe Lopomo, Luca Rigotti, Chris Shannon

http://arxiv.org/abs/2108.12633v1, http://arxiv.org/pdf/2108.12633v1

econ.TH

th

This paper investigates stochastic continuous time contests with a twist: the designer requires that contest participants incur some cost to submit their entries. When the designer wishes to maximize the (expected) performance of the top performer, a strictly positive submission fee is optimal. When the designer wishes to maximize total (expected) performance, either the highest submission fee or the lowest submission fee is optimal.

Submission Fees in Risk-Taking Contests

2021-08-30 23:07:59

Mark Whitmeyer

http://arxiv.org/abs/2108.13506v1, http://arxiv.org/pdf/2108.13506v1

econ.TH

th

Information policies such as scores, ratings, and recommendations are increasingly shaping society's choices in high-stakes domains. We provide a framework to study the welfare implications of information policies on a population of heterogeneous individuals. We define and characterize the Bayes welfare set, consisting of the population's utility profiles that are feasible under some information policy. The Pareto frontier of this set can be recovered by a series of standard Bayesian persuasion problems, in which a utilitarian planner takes the role of the information designer. We provide necessary and sufficient conditions under which an information policy exists that Pareto dominates the no-information policy. We illustrate our results with applications to data leakage, price discrimination, and credit ratings.

Persuasion and Welfare

2021-09-07 15:51:58

Laura Doval, Alex Smolin

http://arxiv.org/abs/2109.03061v4, http://arxiv.org/pdf/2109.03061v4

econ.TH

th

The inventories carried in a supply chain as a strategic tool to influence the competing firms are considered to be strategic inventories (SI). We present a two-period game-theoretic supply chain model, in which a singular manufacturer supplies products to a pair of identical Cournot duopolistic retailers. We show that the SI carried by the retailers under dynamic contract is Pareto-dominating for the manufacturer, retailers, consumers, the channel, and the society as well. We also find that the retailer's SI, however, can be eliminated when the manufacturer commits wholesale contract or inventory holding cost is too high. In comparing the cases with and without downstream competition, we also show that the downstream Cournot duopoly undermines the retailers in profits, but benefits all others.

Strategic Inventories in a Supply Chain with Downstream Cournot Duopoly

2021-09-15 01:21:29

Xiaowei Hu, Jaejin Jang, Nabeel Hamoud, Amirsaman Bajgiran

http://dx.doi.org/10.1504/IJOR.2021.119934, http://arxiv.org/abs/2109.06995v2, http://arxiv.org/pdf/2109.06995v2

econ.GN

th

This paper proposes a new approach to training recommender systems called deviation-based learning. The recommender and rational users have different knowledge. The recommender learns user knowledge by observing what action users take upon receiving recommendations. Learning eventually stalls if the recommender always suggests a choice: Before the recommender completes learning, users start following the recommendations blindly, and their choices do not reflect their knowledge. The learning rate and social welfare improve substantially if the recommender abstains from recommending a particular choice when she predicts that multiple alternatives will produce a similar payoff.

Deviation-Based Learning: Training Recommender Systems Using Informed User Choice

2021-09-20 22:51:37

Junpei Komiyama, Shunya Noda

http://arxiv.org/abs/2109.09816v2, http://arxiv.org/pdf/2109.09816v2

econ.TH

th

We consider the problem of revenue-maximizing Bayesian auction design with several bidders having independent private values over several items. We show that it can be reduced to the problem of continuous optimal transportation introduced by Beckmann (1952) where the optimal transportation flow generalizes the concept of ironed virtual valuations to the multi-item setting. We establish the strong duality between the two problems and the existence of solutions. The results rely on insights from majorization and optimal transportation theories and on the characterization of feasible interim mechanisms by Hart and Reny (2015).

Beckmann's approach to multi-item multi-bidder auctions

2022-03-14 06:30:58

Alexander V. Kolesnikov, Fedor Sandomirskiy, Aleh Tsyvinski, Alexander P. Zimin

http://arxiv.org/abs/2203.06837v2, http://arxiv.org/pdf/2203.06837v2

econ.TH

th

We introduce NEM X, an inclusive retail tariff model that captures features of existing net energy metering (NEM) policies. It is shown that the optimal prosumer decision has three modes: (a) the net-consuming mode where the prosumer consumes more than its behind-the-meter distributed energy resource (DER) production when the DER production is below a predetermined lower threshold, (b) the net-producing mode where the prosumer consumes less than its DER production when the DER production is above a predetermined upper threshold, and (c) the net-zero energy mode where the prosumer's consumption matches to its DER generation when its DER production is between the lower and upper thresholds. Both thresholds are obtained in closed-form. Next, we analyze the regulator's rate-setting process that determines NEM X parameters such as retail/sell rates, fixed charges, and price differentials in time-of-use tariffs' on and off-peak periods. A stochastic Ramsey pricing program that maximizes social welfare subject to the revenue break-even constraint for the regulated utility is formulated. Performance of several NEM X policies is evaluated using real and synthetic data to illuminate impacts of NEM policy designs on social welfare, cross-subsidies of prosumers by consumers, and payback time of DER investments that affect long-run DER adoptions.

On Net Energy Metering X: Optimal Prosumer Decisions, Social Welfare, and Cross-Subsidies

2021-09-21 08:58:59

Ahmed S. Alahmed, Lang Tong

http://arxiv.org/abs/2109.09977v4, http://arxiv.org/pdf/2109.09977v4

eess.SY

th

An individual can only experience regret if she learns about an unchosen alternative. In many situations, learning about an unchosen alternative is possible only if someone else chose it. We develop a model where the ex-post information available to each regret averse individual depends both on their own choice and on the choices of others, as others can reveal ex-post information about what might have been. This implies that what appears to be a series of isolated single-person decision problems is in fact a rich multi-player behavioural game, the regret game, where the psychological payoffs that depend on ex-post information are interconnected. For an open set of parameters, the regret game is a coordination game with multiple equilibria, despite the fact that all individuals possess a uniquely optimal choice in isolation. We experimentally test this prediction and find support for it.

Ignorance is Bliss: A Game of Regret

2021-09-22 21:34:55

Claudia Cerrone, Francesco Feri, Philip R. Neary

http://arxiv.org/abs/2109.10968v3, http://arxiv.org/pdf/2109.10968v3

econ.TH

th

I extend the concept of absorptive capacity, used in the analysis of firms, to a framework applicable to the national level. First, employing confirmatory factor analyses on 47 variables, I build 13 composite factors crucial to measuring six national level capacities: technological capacity, financial capacity, human capacity, infrastructural capacity, public policy capacity, and social capacity. My data cover most low- and middle-income- economies (LMICs), eligible for the World Bank's International Development Association (IDA) support between 2005 and 2019. Second, I analyze the relationship between the estimated capacity factors and economic growth while controlling for some of the incoming flows from abroad and other confounders that might influence the relationship. Lastly, I conduct K-means cluster analysis and then analyze the results alongside regression estimates to glean patterns and classifications within the LMICs. Results indicate that enhancing infrastructure (ICT, energy, trade, and transport), financial (apparatus and environment), and public policy capacities is a prerequisite for attaining economic growth. Similarly, I find improving human capital with specialized skills positively impacts economic growth. Finally, by providing a ranking of which capacity is empirically more important for economic growth, I offer suggestions to governments with limited budgets to make wise investments. Likewise, my findings inform international policy and monetary bodies on how they could better channel their funding in LMICs to achieve sustainable development goals and boost shared prosperity.

Absorptive capacities and economic growth in low and middle income economies

2021-09-23 20:49:51

Muhammad Salar Khan

http://arxiv.org/abs/2109.11550v1, http://arxiv.org/pdf/2109.11550v1

econ.GN

th

Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to realworld problems because of their complexity and unrealistic assumptions about human behaviors. Here we propose a fair division method from a completely different perspective, using the Boltzmann distribution. The Boltzmann distribution adopted from the physical sciences gives the most probable and unbiased distribution derived from a goods-centric, rather than a player-centric, division process. The mathematical model of the Boltzmann fair division was developed for both homogeneous and heterogeneous division problems, and the players' key factors (contributions, needs, and preferences) could be successfully integrated. We show that the Boltzmann fair division is a well-balanced division method maximizing the players' total utility, and it could be easily finetuned and applicable to complex real-world problems such as income/wealth redistribution or international negotiations on fighting climate change.

The Boltzmann fair division for distributive justice

2021-09-24 15:17:04

Ji-Won Park, Jaeup U. Kim, Cheol-Min Ghim, Chae Un Kim

http://arxiv.org/abs/2109.11917v2, http://arxiv.org/pdf/2109.11917v2

econ.GN

th

Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. In this paper, we cast the bilateral trade problem in a regret minimization framework over $T$ rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed-price in hindsight. More precisely, we prove the following tight bounds on the regret: - $\Theta(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms). - $\Theta(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. - $\Theta(T)$ for realistic feedback and seller/buyer valuations with bounded densities. - $\Theta(T)$ for realistic feedback and independent seller/buyer valuations. - $\Theta(T)$ for the adversarial setting.

Bilateral Trade: A Regret Minimization Perspective

2021-09-09 01:11:48

Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi

http://arxiv.org/abs/2109.12974v1, http://arxiv.org/pdf/2109.12974v1

cs.GT

th

Matching markets are of particular interest in computer science and economics literature as they are often used to model real-world phenomena where we aim to equitably distribute a limited amount of resources to multiple agents and determine these distributions efficiently. Although it has been shown that finding market clearing prices for Fisher markets with indivisible goods is NP-hard, there exist polynomial-time algorithms able to compute these prices and allocations when the goods are divisible and the utility functions are linear. We provide a promising research direction toward the development of a market that simulates buyers' preferences that vary according to the bundles of goods allocated to other buyers. Our research aims to elucidate unique ways in which the theory of matching markets can be extended to account for more complex and often counterintuitive microeconomic phenomena.

Matching Markets

2021-09-30 08:13:27

Andrew Yang, Bruce Changlong Xu, Ivan Villa-Renteria

http://arxiv.org/abs/2109.14850v1, http://arxiv.org/pdf/2109.14850v1

cs.GT

th

We study an information design problem for a non-atomic service scheduling game. The service starts at a random time and there is a continuum of agent population who have a prior belief about the service start time but do not observe the actual realization of it. The agents want to make decisions of when to join the queue in order to avoid long waits in the queue or not to arrive earlier than the service has started. There is a planner who knows when the service starts and makes suggestions to the agents about when to join the queue through an obedient direct signaling strategy, in order to minimize the average social cost. We characterize the full information and the no information equilibria and we show in what conditions it is optimal for the planner to reveal the full information to the agents. Further, by imposing appropriate assumptions on the model, we formulate the information design problem as a generalized problem of moments (GPM) and use computational tools developed for such problems to solve the problem numerically.

Information Design for a Non-atomic Service Scheduling Game

2021-10-01 00:18:24

Nasimeh Heydaribeni, Ketan Savla

http://arxiv.org/abs/2110.00090v1, http://arxiv.org/pdf/2110.00090v1

eess.SY

th

In the setting where we want to aggregate people's subjective evaluations, plurality vote may be meaningless when a large amount of low-effort people always report "good" regardless of the true quality. "Surprisingly popular" method, picking the most surprising answer compared to the prior, handle this issue to some extent. However, it is still not fully robust to people's strategies. Here in the setting where a large number of people are asked to answer a small number of multi-choice questions (multi-task, large group), we propose an information aggregation method that is robust to people's strategies. Interestingly, this method can be seen as a rotated "surprisingly popular". It is based on a new clustering method, Determinant MaxImization (DMI)-clustering, and a key conceptual idea that information elicitation without ground-truth can be seen as a clustering problem. Of independent interest, DMI-clustering is a general clustering method that aims to maximize the volume of the simplex consisting of each cluster's mean multiplying the product of the cluster sizes. We show that DMI-clustering is invariant to any non-degenerate affine transformation for all data points. When the data point's dimension is a constant, DMI-clustering can be solved in polynomial time. In general, we present a simple heuristic for DMI-clustering which is very similar to Lloyd's algorithm for k-means. Additionally, we also apply the clustering idea in the single-task setting and use the spectral method to propose a new aggregation method that utilizes the second-moment information elicited from the crowds.

Information Elicitation Meets Clustering

2021-10-03 11:47:55

Yuqing Kong

http://arxiv.org/abs/2110.00952v1, http://arxiv.org/pdf/2110.00952v1

cs.GT

th

Condorcet's jury theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter's independent probability of voting for that outcome is greater than 0.5. Yet, in situations where direct voting systems are infeasible, such as due to high implementation and infrastructure costs, hierarchical voting systems provide a reasonable alternative. We study differences in outcome precision between hierarchical and direct voting systems for varying group sizes, abstention rates, and voter competencies. Using asymptotic expansions of the derivative of the reliability function (or Banzhaf number), we first prove that indirect systems differ most from their direct counterparts when group size and number are equal to each other, and therefore to $\sqrt{N_{\rm d}}$, where $N_{\rm d}$ is the total number of voters in the direct system. In multitier systems, we prove that this difference is maximized when group size equals $\sqrt[n]{N_{\rm d}}$, where $n$ is the number of hierarchical levels. Second, we show that while direct majority rule always outperforms hierarchical voting for homogeneous electorates that vote with certainty, as group numbers and size increase, hierarchical majority voting gains in its ability to represent all eligible voters. Furthermore, when voter abstention and competency are correlated within groups, hierarchical systems often outperform direct voting, which we show by using a generating function approach that is able to analytically characterize heterogeneous voting systems.

Tradeoffs in Hierarchical Voting Systems

2021-10-05 22:01:52

Lucas Böttcher, Georgia Kernell

http://dx.doi.org/10.1177/26339137221133401, http://arxiv.org/abs/2110.02298v1, http://arxiv.org/pdf/2110.02298v1

math.CO

th

In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.

Feature Selection by a Mechanism Design

2021-10-06 02:53:14

Xingwei Hu

http://arxiv.org/abs/2110.02419v1, http://arxiv.org/pdf/2110.02419v1

stat.ML

th

A modelling framework, based on the theory of signal processing, for characterising the dynamics of systems driven by the unravelling of information is outlined, and is applied to describe the process of decision making. The model input of this approach is the specification of the flow of information. This enables the representation of (i) reliable information, (ii) noise, and (iii) disinformation, in a unified framework. Because the approach is designed to characterise the dynamics of the behaviour of people, it is possible to quantify the impact of information control, including those resulting from the dissemination of disinformation. It is shown that if a decision maker assigns an exceptionally high weight on one of the alternative realities, then under the Bayesian logic their perception hardly changes in time even if evidences presented indicate that this alternative corresponds to a false reality. Thus confirmation bias need not be incompatible with Bayesian updating. By observing the role played by noise in other areas of natural sciences, where noise is used to excite the system away from false attractors, a new approach to tackle the dark forces of fake news is proposed.

Noise, fake news, and tenacious Bayesians

2021-10-05 19:11:08

Dorje C. Brody

http://arxiv.org/abs/2110.03432v3, http://arxiv.org/pdf/2110.03432v3

econ.TH

th

The Shapley value, one of the well-known allocation rules in game theory, does not take into account information about the structure of the graph, so by using the Shapley value for each hyperedge, we introduce a new allocation rule by considering their first-order combination. We proved that some of the properties that hold for Shapley and Myerson values also hold for our allocation rule. In addition, we found the relationship between our allocation rule and the Forman curvature, which plays an important role in discrete geometry.

New allocation rule of directed hypergraphs

2021-10-13 08:29:47

Taiki Yamada

http://arxiv.org/abs/2110.06506v3, http://arxiv.org/pdf/2110.06506v3

cs.GT

th

In this paper, we study a matching market model on a bipartite network where agents on each side arrive and depart stochastically by a Poisson process. For such a dynamic model, we design a mechanism that decides not only which agents to match, but also when to match them, to minimize the expected number of unmatched agents. The main contribution of this paper is to achieve theoretical bounds on the performance of local mechanisms with different timing properties. We show that an algorithm that waits to thicken the market, called the $\textit{Patient}$ algorithm, is exponentially better than the $\textit{Greedy}$ algorithm, i.e., an algorithm that matches agents greedily. This means that waiting has substantial benefits on maximizing a matching over a bipartite network. We remark that the Patient algorithm requires the planner to identify agents who are about to leave the market, and, under the requirement, the Patient algorithm is shown to be an optimal algorithm. We also show that, without the requirement, the Greedy algorithm is almost optimal. In addition, we consider the $\textit{1-sided algorithms}$ where only an agent on one side can attempt to match. This models a practical matching market such as a freight exchange market and a labor market where only agents on one side can make a decision. For this setting, we prove that the Greedy and Patient algorithms admit the same performance, that is, waiting to thicken the market is not valuable. This conclusion is in contrast to the case where agents on both sides can make a decision and the non-bipartite case by [Akbarpour et al.,$~\textit{Journal of Political Economy}$, 2020].

Dynamic Bipartite Matching Market with Arrivals and Departures

2021-10-21 02:44:04

Naonori Kakimura, Donghao Zhu

http://arxiv.org/abs/2110.10824v1, http://arxiv.org/pdf/2110.10824v1

cs.DS

th

We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show that if the players' payoffs whilst in "war" vary stochastically and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This is true irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model. In contrast, when the players' flow payoffs are deterministic or their exit payoffs are homogeneous, the game admits equilibria in pure and mixed strategies.

The Absence of Attrition in a War of Attrition under Complete Information

2021-10-22 21:55:39

George Georgiadis, Youngsoo Kim, H. Dharma Kwon

http://dx.doi.org/10.1016/j.geb.2021.11.004, http://arxiv.org/abs/2110.12013v2, http://arxiv.org/pdf/2110.12013v2

math.OC

th

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an $\alpha$ factor. If no blocking committee exists under this definition, we call this an $\alpha$-core. Our main result is that an $\alpha$-core, for $\alpha < 67.37$, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to $\alpha < 9.27$ for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of $\alpha > 1.015$ for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

Approximate Core for Committee Selection via Multilinear Extension and Market Clearing

2021-10-24 20:40:20

Kamesh Munagala, Yiheng Shen, Kangning Wang, Zhiyi Wang

http://arxiv.org/abs/2110.12499v1, http://arxiv.org/pdf/2110.12499v1

cs.GT

th

In this paper I investigate a Bayesian inverse problem in the specific setting of a price setting monopolist facing a randomly growing demand in multiple possibly interconnected markets. Investigating the Value of Information of a signal to the monopolist in a fully dynamic discrete model employing the Kalman-Bucy-Stratonovich filter, we find that it may be non-monotonic in the variance of the signal. In the classical static settings of the Value of Information literature this relationship may be convex or concave, but is always monotonic. The existence of the non-monotonicity depends critically on the exogenous growth rate of the system.

Expanding Multi-Market Monopoly and Nonconcavity in the Value of Information

2021-11-01 14:20:09

Stefan Behringer

http://arxiv.org/abs/2111.00839v1, http://arxiv.org/pdf/2111.00839v1

econ.TH

th

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives.

Surreal Decisions

2021-10-23 21:37:20

Eddy Keming Chen, Daniel Rubio

http://dx.doi.org/10.1111/phpr.12510, http://arxiv.org/abs/2111.00862v1, http://arxiv.org/pdf/2111.00862v1

cs.AI

th

We focus on a simple, one-dimensional collective decision problem (often referred to as the facility location problem) and explore issues of strategyproofness and proportionality-based fairness. We introduce and analyze a hierarchy of proportionality-based fairness axioms of varying strength: Individual Fair Share (IFS), Unanimous Fair Share (UFS), Proportionality (as in Freeman et al, 2021), and Proportional Fairness (PF). For each axiom, we characterize the family of mechanisms that satisfy the axiom and strategyproofness. We show that imposing strategyproofness renders many of the axioms to be equivalent: the family of mechanisms that satisfy proportionality, unanimity, and strategyproofness is equivalent to the family of mechanisms that satisfy UFS and strategyproofness, which, in turn, is equivalent to the family of mechanisms that satisfy PF and strategyproofness. Furthermore, there is a unique such mechanism: the Uniform Phantom mechanism, which is studied in Freeman et al. (2021). We also characterize the outcomes of the Uniform Phantom mechanism as the unique (pure) equilibrium outcome for any mechanism that satisfies continuity, strict monotonicity, and UFS. Finally, we analyze the approximation guarantees, in terms of optimal social welfare and minimum total cost, obtained by mechanisms that are strategyproof and satisfy each proportionality-based fairness axiom. We show that the Uniform Phantom mechanism provides the best approximation of the optimal social welfare (and also minimum total cost) among all mechanisms that satisfy UFS.

Strategyproof and Proportionally Fair Facility Location

2021-11-02 15:41:32

Haris Aziz, Alexander Lam, Barton E. Lee, Toby Walsh

http://arxiv.org/abs/2111.01566v3, http://arxiv.org/pdf/2111.01566v3

cs.GT

th

Govindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound.

A Finite Characterization of Perfect Equilibria

2021-11-02 17:58:06

Ivonne Callejas, Srihari Govindan, Lucas Pahl

http://arxiv.org/abs/2111.01638v1, http://arxiv.org/pdf/2111.01638v1

econ.TH

th

The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternatives is relatively large compared to the number of voters. In contrast to the Gibbard-Satterthwaite theorem, many of the rules we examined are not obviously manipulable. This reflects the relatively easier satisfiability of the notion and the zero information assumption of not obvious manipulability, as opposed to the perfect information assumption of strategyproofness. We also present algorithmic results for computing obvious manipulations and report on experiments.

Obvious Manipulability of Voting Rules

2021-11-03 05:41:48

Haris Aziz, Alexander Lam

http://dx.doi.org/10.1007/978-3-030-87756-9_12, http://arxiv.org/abs/2111.01983v3, http://arxiv.org/pdf/2111.01983v3

cs.GT

th

We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism.

Approximately Efficient Bilateral Trade

2021-11-05 19:49:45

Yuan Deng, Jieming Mao, Balasubramanian Sivan, Kangning Wang

http://arxiv.org/abs/2111.03611v1, http://arxiv.org/pdf/2111.03611v1

cs.GT

th

In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the cause-effect relations within the data. Regression analysis, however, is generally for correlation relation, and very few researches have focused on variance analysis for causality discovery. We first set up an equilibrium for the cause-effect relations using a fictitious vector autoregressive model. In the equilibrium, long-run relations are identified from noise, and spurious ones are negligibly close to zero. The solution, called causality distribution, measures the relative strength causing the movement of all series or specific affected ones. If a group of exogenous data affects the others but not vice versa, then, in theory, the causality distribution for other variables is necessarily zero. The hypothesis test of zero causality is the rule to decide a variable is endogenous or not. Our new approach has high accuracy in identifying the true cause-effect relations among the data in the simulation studies. We also apply the approach to estimating the causal factors' contribution to climate change.

Decoding Causality by Fictitious VAR Modeling

2021-11-15 01:43:02

Xingwei Hu

http://arxiv.org/abs/2111.07465v2, http://arxiv.org/pdf/2111.07465v2

stat.ML

th

A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is $f(A)$ and if the output model $B$ is $f(B)$, then the output of the model obtained by aggregating $A$ and $B$ must be a weighted average of $f(A)$ and $f(B)$. Similarly, a natural notion of rationality for aggregating preferences of ensembles of experts is that, for all (possibly aggregated) experts $A$ and $B$, and all possible choices $x$ and $y$, if both $A$ and $B$ prefer $x$ over $y$, then the expert obtained by aggregating $A$ and $B$ must also prefer $x$ over $y$. Rational aggregation is an important element of uncertainty quantification, and it lies behind many seemingly different results in economic theory: spanning social choice, belief formation, and individual decision making. Three examples of rational aggregation rules are as follows. (1) Give each individual model (expert) a weight (a score) and use weighted averaging to aggregate individual or finite ensembles of models (experts). (2) Order/rank individual model (expert) and let the aggregation of a finite ensemble of individual models (experts) be the highest-ranked individual model (expert) in that ensemble. (3) Give each individual model (expert) a weight, introduce a weak order/ranking over the set of models/experts, aggregate $A$ and $B$ as the weighted average of the highest-ranked models (experts) in $A$ or $B$. Note that (1) and (2) are particular cases of (3). In this paper, we show that all rational aggregation rules are of the form (3). This result unifies aggregation procedures across different economic environments. Following the main representation, we show applications and extensions of our representation in various separated economics topics such as belief formation, choice theory, and social welfare economics.

Aggregation of Models, Choices, Beliefs, and Preferences

2021-11-23 06:26:42

Hamed Hamze Bajgiran, Houman Owhadi

http://arxiv.org/abs/2111.11630v1, http://arxiv.org/pdf/2111.11630v1

econ.TH

th

Securities borrowing and lending are critical to proper functioning of securities markets. To alleviate securities owners' exposure to borrower default risk, overcollateralization and indemnification are provided by the borrower and the lending agent respectively. Haircuts as the level of overcollateralization and the cost of indemnification are naturally interrelated: the higher haircut is, the lower cost shall become. This article presents a method of quantifying their relationship. Borrower dependent haircuts satisfying the lender's credit risk appetite are computed for US Treasuries and main equities by applying a repo haircut model to bilateral securities lending transactions. Indemnification is designed to fulfill a triple-A risk appetite when the transaction haircut fails to deliver. The cost of indemnification consists of a risk charge, a capital charge, and a funding charge, each corresponding to the expected loss, the economic capital, and the redundant fund needed to arrive at the triple-A haircut.

Securities Lending Haircuts and Indemnification Pricing

2021-11-25 22:15:37

Wujiang Lou

http://dx.doi.org/10.2139/ssrn.3682930, http://arxiv.org/abs/2111.13228v1, http://arxiv.org/pdf/2111.13228v1

q-fin.MF

th

The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory.

A Resolution of St. Petersburg Paradox

2021-11-24 16:59:32

V. I. Yukalov

http://arxiv.org/abs/2111.14635v1, http://arxiv.org/pdf/2111.14635v1

math.OC

th

We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of these polytopes. Such polytopes arise from identifying (topologically) equivalent mixed strategies of a normal form game.

Polytope-form games and Index/Degree Theories for Extensive-form games

2022-01-06 18:28:08

Lucas Pahl

http://arxiv.org/abs/2201.02098v4, http://arxiv.org/pdf/2201.02098v4

econ.TH

th

A preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan (resp. $d$-Euclidean) if both the alternatives and the voters can be placed into the $d$-dimensional space such that between each pair of alternatives, every voter prefers the one which has a shorter Manhattan (resp. Euclidean) distance to the voter. Following Bogomolnaia and Laslier [Journal of Mathematical Economics, 2007] and Chen and Grottke [Social Choice and Welfare, 2021] who look at $d$-Euclidean preference profiles, we study which preference profiles are $d$-Manhattan depending on the values $m$ and $n$. First, we show that each preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan whenever $d$ $\geq$ min($n$, $m$-$1$). Second, for $d = 2$, we show that the smallest non $d$-Manhattan preference profile has either three voters and six alternatives, or four voters and five alternatives, or five voters and four alternatives. This is more complex than the case with $d$-Euclidean preferences (see [Bogomolnaia and Laslier, 2007] and [Bulteau and Chen, 2020].

Multidimensional Manhattan Preferences

2022-01-24 16:52:38

Jiehua Chen, Martin Nöllenburg, Sofia Simola, Anaïs Villedieu, Markus Wallinger

http://arxiv.org/abs/2201.09691v1, http://arxiv.org/pdf/2201.09691v1

cs.MA

th

We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a version of Experience-Weighted Attraction (EWA) algorithm. The dynamics is characterized by two parameters: the (population) intensity of choice $a>0$ capturing the economic rationality of the total population of agents and a discount factor $\sigma\in [0,1]$ capturing a type of memory loss where past outcomes matter exponentially less than the recent ones. Finally, our system adds a third parameter $b \in (0,1)$, which captures the asymmetry of the cost functions of the two resources. It is the proportion of the agents using the first resource at Nash equilibrium, with $b=1/2$ capturing a symmetric network. Within this simple framework, we show a plethora of bifurcation phenomena where behavioral dynamics destabilize from global convergence to equilibrium, to limit cycles or even (formally proven) chaos as a function of the parameters $a$, $b$ and $\sigma$. Specifically, we show that for any discount factor $\sigma$ the system will be destabilized for a sufficiently large intensity of choice $a$. Although for discount factor $\sigma=0$ almost always (i.e., $b \neq 1/2$) the system will become chaotic, as $\sigma$ increases the chaotic regime will give place to the attracting periodic orbit of period 2. Therefore, memory loss can simplify game dynamics and make the system predictable. We complement our theoretical analysis with simulations and several bifurcation diagrams that showcase the unyielding complexity of the population dynamics (e.g., attracting periodic orbits of different lengths) even in the simplest possible potential games.

Unpredictable dynamics in congestion games: memory loss can prevent chaos

2022-01-26 18:07:03

Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, Michal Misiurewicz, Georgios Piliouras

http://arxiv.org/abs/2201.10992v2, http://arxiv.org/pdf/2201.10992v2

cs.GT

th

We propose and solve a negotiation model of multiple players facing many alternative solutions. The model can be generalized to many relevant circumstances where stakeholders' interests partially overlap and partially oppose. We also show that the model can be mapped into the well-known directed percolation and directed polymers problems. Moreover, many statistical mechanics tools, such as the Replica method, can be fruitfully employed. Studying our negotiation model can enlighten the links between social-economic phenomena and traditional statistical mechanics and help to develop new perspectives and tools in the fertile interdisciplinary field.

Negotiation problem

2022-01-29 20:06:45

Izat B. Baybusinov, Enrico Maria Fenoaltea, Yi-Cheng Zhang

http://dx.doi.org/10.1016/j.physa.2021.126806, http://arxiv.org/abs/2201.12619v1, http://arxiv.org/pdf/2201.12619v1

physics.soc-ph

th

We give new characterizations of core imputations for the following games: * The assignment game. * Concurrent games, i.e., general graph matching games having non-empty core. * The unconstrained bipartite $b$-matching game (edges can be matched multiple times). * The constrained bipartite $b$-matching game (edges can be matched at most once). The classic paper of Shapley and Shubik \cite{Shapley1971assignment} showed that core imputations of the assignment game are precisely optimal solutions to the dual of the LP-relaxation of the game. Building on this, Deng et al. \cite{Deng1999algorithms} gave a general framework which yields analogous characterizations for several fundamental combinatorial games. Interestingly enough, their framework does not apply to the last two games stated above. In turn, we show that some of the core imputations of these games correspond to optimal dual solutions and others do not. This leads to the tantalizing question of understanding the origins of the latter. We also present new characterizations of the profits accrued by agents and teams in core imputations of the first two games. Our characterization for the first game is stronger than that for the second; the underlying reason is that the characterization of vertices of the Birkhoff polytope is stronger than that of the Balinski polytope.

New Characterizations of Core Imputations of Matching and $b$-Matching Games

2022-02-01 21:08:50

Vijay V. Vazirani

http://arxiv.org/abs/2202.00619v12, http://arxiv.org/pdf/2202.00619v12

cs.GT

th

The Non-Fungible Token (NFT) is viewed as one of the important applications of blockchain technology. Although NFT has a large market scale and multiple practical standards, several limitations of the existing mechanism in NFT markets exist. This work proposes a novel securitization and repurchase scheme for NFT to overcome these limitations. We first provide an Asset-Backed Securities (ABS) solution to settle the limitations of non-fungibility of NFT. Our securitization design aims to enhance the liquidity of NFTs and enable Oracles and Automatic Market Makers (AMMs) for NFTs. Then we propose a novel repurchase protocol for a participant owing a portion of NFT to repurchase other shares to obtain the complete ownership. As participants may strategically bid during the acquisition process, our repurchase process is formulated as a Stackelberg game to explore the equilibrium prices. We also provide solutions to handle difficulties at market such as budget constraints and lazy bidders.

ABSNFT: Securitization and Repurchase Scheme for Non-Fungible Tokens Based on Game Theoretical Analysis

2022-02-04 18:46:03

Hongyin Chen, Yukun Cheng, Xiaotie Deng, Wenhan Huang, Linxuan Rong

http://arxiv.org/abs/2202.02199v2, http://arxiv.org/pdf/2202.02199v2

cs.GT

th

We develop a tractable model for studying strategic interactions between learning algorithms. We uncover a mechanism responsible for the emergence of algorithmic collusion. We observe that algorithms periodically coordinate on actions that are more profitable than static Nash equilibria. This novel collusive channel relies on an endogenous statistical linkage in the algorithms' estimates which we call spontaneous coupling. The model's parameters predict whether the statistical linkage will appear, and what market structures facilitate algorithmic collusion. We show that spontaneous coupling can sustain collusion in prices and market shares, complementing experimental findings in the literature. Finally, we apply our results to design algorithmic markets.

Artificial Intelligence and Spontaneous Collusion

2022-02-12 03:50:15

Martino Banchio, Giacomo Mantegazza

http://arxiv.org/abs/2202.05946v5, http://arxiv.org/pdf/2202.05946v5

econ.TH

th

Motivated by online advertising auctions, we study auction design in repeated auctions played by simple Artificial Intelligence algorithms (Q-learning). We find that first-price auctions with no additional feedback lead to tacit-collusive outcomes (bids lower than values), while second-price auctions do not. We show that the difference is driven by the incentive in first-price auctions to outbid opponents by just one bid increment. This facilitates re-coordination on low bids after a phase of experimentation. We also show that providing information about lowest bid to win, as introduced by Google at the time of switch to first-price auctions, increases competitiveness of auctions.

Artificial Intelligence and Auction Design

2022-02-12 03:54:40

Martino Banchio, Andrzej Skrzypacz

http://arxiv.org/abs/2202.05947v1, http://arxiv.org/pdf/2202.05947v1

econ.TH

th

For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the likelihood for an election to be influenced when the votes follow certain distributions, especially the likelihood of being manipulable by a single voter under the i.i.d. uniform distribution, known as the Impartial Culture (IC). In this paper, we extend previous studies in three aspects: (1) we propose a more general semi-random model, where a distribution adversary chooses a worst-case distribution and then a contamination adversary modifies up to $\psi$ portion of the data, (2) we consider many coalitional influence problems, including coalitional manipulation, margin of victory, and various vote controls and bribery, and (3) we consider arbitrary and variable coalition size $B$. Our main theorem provides asymptotically tight bounds on the semi-random likelihood of the existence of a size-$B$ coalition that can successfully influence the election under a wide range of voting rules. Applications of the main theorem and its proof techniques resolve long-standing open questions about the likelihood of coalitional manipulability under IC, by showing that the likelihood is $\Theta\left(\min\left\{\frac{B}{\sqrt n}, 1\right\}\right)$ for many commonly-studied voting rules. The main technical contribution is a characterization of the semi-random likelihood for a Poisson multinomial variable (PMV) to be unstable, which we believe to be a general and useful technique with independent interest.

The Impact of a Coalition: Assessing the Likelihood of Voter Influence in Large Elections

2022-02-14 00:27:22

Lirong Xia

http://arxiv.org/abs/2202.06411v4, http://arxiv.org/pdf/2202.06411v4

econ.TH

th

In this paper, we analyze the problem of how to adapt the concept of proportionality to situations where several perfectly divisible resources have to be allocated among certain set of agents that have exactly one claim which is used for all resources. In particular, we introduce the constrained proportional awards rule, which extend the classical proportional rule to these situations. Moreover, we provide an axiomatic characterization of this rule.

On proportionality in multi-issue problems with crossed claims

2022-02-20 20:57:40

Rick K. Acosta-Vega, Encarnación Algaba, Joaquín Sánchez-Soriano

http://arxiv.org/abs/2202.09877v1, http://arxiv.org/pdf/2202.09877v1

math.OC

th

In today's economy, it becomes important for Internet platforms to consider the sequential information design problem to align its long term interest with incentives of the gig service providers. This paper proposes a novel model of sequential information design, namely the Markov persuasion processes (MPPs), where a sender, with informational advantage, seeks to persuade a stream of myopic receivers to take actions that maximizes the sender's cumulative utilities in a finite horizon Markovian environment with varying prior and utility functions. Planning in MPPs thus faces the unique challenge in finding a signaling policy that is simultaneously persuasive to the myopic receivers and inducing the optimal long-term cumulative utilities of the sender. Nevertheless, in the population level where the model is known, it turns out that we can efficiently determine the optimal (resp. $\epsilon$-optimal) policy with finite (resp. infinite) states and outcomes, through a modified formulation of the Bellman equation. Our main technical contribution is to study the MPP under the online reinforcement learning (RL) setting, where the goal is to learn the optimal signaling policy by interacting with with the underlying MPP, without the knowledge of the sender's utility functions, prior distributions, and the Markov transition kernels. We design a provably efficient no-regret learning algorithm, the Optimism-Pessimism Principle for Persuasion Process (OP4), which features a novel combination of both optimism and pessimism principles. Our algorithm enjoys sample efficiency by achieving a sublinear $\sqrt{T}$-regret upper bound. Furthermore, both our algorithm and theory can be applied to MPPs with large space of outcomes and states via function approximation, and we showcase such a success under the linear setting.

Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning

2022-02-22 08:41:43

Jibang Wu, Zixuan Zhang, Zhe Feng, Zhaoran Wang, Zhuoran Yang, Michael I. Jordan, Haifeng Xu

http://arxiv.org/abs/2202.10678v1, http://arxiv.org/pdf/2202.10678v1

cs.AI

th

Reputation-based cooperation on social networks offers a causal mechanism between graph properties and social trust. Recent papers on the `structural microfoundations` of the society used this insight to show how demographic processes, such as falling fertility, urbanisation, and migration, can alter the logic of human societies. This paper demonstrates the underlying mechanism in a way that is accessible to scientists not specialising in networks. Additionally, the paper shows that, when the size and degree of the network is fixed (i.e., all graphs have the same number of agents, who all have the same number of connections), it is the clustering coefficient that drives differences in how cooperative social networks are.

Clustering Drives Cooperation on Reputation Networks, All Else Fixed

2022-03-01 14:37:51

Tamas David-Barrett

http://arxiv.org/abs/2203.00372v1, http://arxiv.org/pdf/2203.00372v1

cs.SI