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th

It is well known that Random Serial Dictatorship is strategy-proof and leads to a Pareto-Efficient outcome. We show that this result breaks down when individuals are allowed to make transfers, and adapt Random Serial Dictatorship to encompass trades between individuals. Strategic analysis of play under the new mechanisms we define is given, accompanied by simulations to quantify the gains from trade.

Random Serial Dictatorship with Transfers

2023-12-13 12:14:48

Sudharsan Sundar, Eric Gao, Trevor Chow, Matthew Ding

http://arxiv.org/abs/2312.07999v1, http://arxiv.org/pdf/2312.07999v1

cs.GT

th

In approval-based committee (ABC) voting, the goal is to choose a subset of predefined size of the candidates based on the voters' approval preferences over the candidates. While this problem has attracted significant attention in recent years, the incentives for voters to participate in an election for a given ABC voting rule have been neglected so far. This paper is thus the first to explicitly study this property, typically called participation, for ABC voting rules. In particular, we show that all ABC scoring rules even satisfy group participation, whereas most sequential rules severely fail participation. We furthermore explore several escape routes to the impossibility for sequential ABC voting rules: we prove for many sequential rules that (i) they satisfy participation on laminar profiles, (ii) voters who approve none of the elected candidates cannot benefit by abstaining, and (iii) it is NP-hard for a voter to decide whether she benefits from abstaining.

Participation Incentives in Approval-Based Committee Elections

2023-12-14 13:32:59

Martin Bullinger, Chris Dong, Patrick Lederer, Clara Mehler

http://arxiv.org/abs/2312.08798v1, http://arxiv.org/pdf/2312.08798v1

cs.GT

th

In approval-based committee (ABC) elections, the goal is to select a fixed-size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. One of the most popular classes of ABC voting rules are ABC scoring rules, which have recently been characterized by Lackner and Skowron (2021). However, this characterization relies on a model where the output is a ranking of committees instead of a set of winning committees and no full characterization of ABC scoring rules exists in the latter standard setting. We address this issue by characterizing two important subclasses of ABC scoring rules in the standard ABC election model, thereby both extending the result of Lackner and Skowron (2021) to the standard setting and refining it to subclasses. In more detail, by relying on a consistency axiom for variable electorates, we characterize (i) the prominent class of Thiele rules and (ii) a new class of ABC voting rules called ballot size weighted approval voting. Based on these theorems, we also infer characterizations of three well-known ABC voting rules, namely multi-winner approval voting, proportional approval voting, and satisfaction approval voting.

Refined Characterizations of Approval-based Committee Scoring Rules

2023-12-14 13:34:07

Chris Dang, Patrick Lederer

http://arxiv.org/abs/2312.08799v1, http://arxiv.org/pdf/2312.08799v1

cs.GT

th

We provide the first large-scale data collection of real-world approval-based committee elections. These elections have been conducted on the Polkadot blockchain as part of their Nominated Proof-of-Stake mechanism and contain around one thousand candidates and tens of thousands of (weighted) voters each. We conduct an in-depth study of application-relevant questions, including a quantitative and qualitative analysis of the outcomes returned by different voting rules. Besides considering proportionality measures that are standard in the multiwinner voting literature, we pay particular attention to less-studied measures of overrepresentation, as these are closely related to the security of the Polkadot network. We also analyze how different design decisions such as the committee size affect the examined measures.

Approval-Based Committee Voting in Practice: A Case Study of (Over-)Representation in the Polkadot Blockchain

2023-12-18 21:15:38

Niclas Boehmer, Markus Brill, Alfonso Cevallos, Jonas Gehrlein, Luis Sánchez-Fernández, Ulrike Schmidt-Kraepelin

http://arxiv.org/abs/2312.11408v2, http://arxiv.org/pdf/2312.11408v2

cs.GT

th

In this note, I introduce Estimated Performance Rating (PR$^e$), a novel system for evaluating player performance in sports and games. PR$^e$ addresses a key limitation of the Tournament Performance Rating (TPR) system, which is undefined for zero or perfect scores in a series of games. PR$^e$ is defined as the rating that solves an optimization problem related to scoring probability, making it applicable for any performance level. The main theorem establishes that the PR$^e$ of a player is equivalent to the TPR whenever the latter is defined. I then apply this system to historically significant win-streaks in association football, tennis, and chess. Beyond sports, PR$^e$ has broad applicability in domains where Elo ratings are used, from college rankings to the evaluation of large language models.

Performance rating in chess, tennis, and other contexts

2023-12-20 04:47:55

Mehmet S. Ismail

http://arxiv.org/abs/2312.12700v1, http://arxiv.org/pdf/2312.12700v1

econ.TH

th

We consider moral hazard problems where a principal has access to rich monitoring data about an agent's action. Rather than focusing on optimal contracts (which are known to in general be complicated), we characterize the optimal rate at which the principal's payoffs can converge to the first-best payoff as the amount of data grows large. Our main result suggests a novel rationale for the widely observed binary wage schemes, by showing that such simple contracts achieve the optimal convergence rate. Notably, in order to attain the optimal convergence rate, the principal must set a lenient cutoff for when the agent receives a high vs. low wage. In contrast, we find that other common contracts where wages vary more finely with observed data (e.g., linear contracts) approximate the first-best at a highly suboptimal rate. Finally, we show that the optimal convergence rate depends only on a simple summary statistic of the monitoring technology. This yields a detail-free ranking over monitoring technologies that quantifies their value for incentive provision in data-rich settings and applies regardless of the agent's specific utility or cost functions.

Monitoring with Rich Data

2023-12-28 05:34:18

Mira Frick, Ryota Iijima, Yuhta Ishii

http://arxiv.org/abs/2312.16789v1, http://arxiv.org/pdf/2312.16789v1

econ.TH

th

We study the problem of screening in decision-making processes under uncertainty, focusing on the impact of adding an additional screening stage, commonly known as a 'gatekeeper.' While our primary analysis is rooted in the context of job market hiring, the principles and findings are broadly applicable to areas such as educational admissions, healthcare patient selection, and financial loan approvals. The gatekeeper's role is to assess applicants' suitability before significant investments are made. Our study reveals that while gatekeepers are designed to streamline the selection process by filtering out less likely candidates, they can sometimes inadvertently affect the candidates' own decision-making process. We explore the conditions under which the introduction of a gatekeeper can enhance or impede the efficiency of these processes. Additionally, we consider how adjusting gatekeeping strategies might impact the accuracy of selection decisions. Our research also extends to scenarios where gatekeeping is influenced by historical biases, particularly in competitive settings like hiring. We discover that candidates confronted with a statistically biased gatekeeping process are more likely to withdraw from applying, thereby perpetuating the previously mentioned historical biases. The study suggests that measures such as affirmative action can be effective in addressing these biases. While centered on hiring, the insights and methodologies from our study have significant implications for a wide range of fields where screening and gatekeeping are integral.

The Gatekeeper Effect: The Implications of Pre-Screening, Self-selection, and Bias for Hiring Processes

2023-12-28 20:54:39

Moran Koren

http://arxiv.org/abs/2312.17167v1, http://arxiv.org/pdf/2312.17167v1

econ.TH

th

The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.

Sequential choice functions and stability problems

2024-01-01 16:08:56

Vladimir I. Danilov

http://arxiv.org/abs/2401.00748v1, http://arxiv.org/pdf/2401.00748v1

math.CO

th

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.

Correlated Equilibria of Classical Strategic Games with Quantum Signals

2003-09-03 02:34:49

Pierfrancesco La Mura

http://dx.doi.org/10.1142/S0219749905000724, http://arxiv.org/abs/quant-ph/0309033v1, http://arxiv.org/pdf/quant-ph/0309033v1

quant-ph

th

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.

Projective Expected Utility

2008-02-22 14:00:20

Pierfrancesco La Mura

http://dx.doi.org/10.1016/j.jmp.2009.02.001, http://arxiv.org/abs/0802.3300v1, http://arxiv.org/pdf/0802.3300v1

quant-ph

th

In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has preferences. Most interesting decision problems, however, do not come with a state space and an outcome space. Indeed, in complex problems it is often far from clear what the state and outcome spaces would be. We present an alternative foundation for decision making, in which the primitive objects of choice are syntactic programs. A representation theorem is proved in the spirit of standard representation theorems, showing that if the DM's preference relation on objects of choice satisfies appropriate axioms, then there exist a set S of states, a set O of outcomes, a way of interpreting the objects of choice as functions from S to O, a probability on S, and a utility function on O, such that the DM prefers choice a to choice b if and only if the expected utility of a is higher than that of b. Thus, the state space and outcome space are subjective, just like the probability and utility; they are not part of the description of the problem. In principle, a modeler can test for SEU behavior without having access to states or outcomes. We illustrate the power of our approach by showing that it can capture decision makers who are subject to framing effects.

Constructive Decision Theory

2009-06-23 21:22:45

Lawrence Blume, David Easley, Joseph Y. Halpern

http://arxiv.org/abs/0906.4316v2, http://arxiv.org/pdf/0906.4316v2

cs.GT

th

We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce Social Learning Equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.

Social learning equilibria

2012-07-25 08:58:32

Elchanan Mossel, Manuel Mueller-Frank, Allan Sly, Omer Tamuz

http://dx.doi.org/10.3982/ECTA16465, http://arxiv.org/abs/1207.5895v4, http://arxiv.org/pdf/1207.5895v4

math.ST

th

We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals, and by observing the actions of their neighbors in a social network. We show that the question of whether or not the agents learn efficiently depends on the topology of the social network. In particular, we identify a geometric "egalitarianism" condition on the social network that guarantees learning in infinite networks, or learning with high probability in large finite networks, in any equilibrium. We also give examples of non-egalitarian networks with equilibria in which learning fails.

Strategic Learning and the Topology of Social Networks

2012-09-25 11:13:59

Elchanan Mossel, Allan Sly, Omer Tamuz

http://dx.doi.org/10.3982/ECTA12058, http://arxiv.org/abs/1209.5527v2, http://arxiv.org/pdf/1209.5527v2

cs.GT

th

We consider the complexity of finding a correlated equilibrium of an $n$-player game in a model that allows the algorithm to make queries on players' payoffs at pure strategy profiles. Randomized regret-based dynamics are known to yield an approximate correlated equilibrium efficiently, namely, in time that is polynomial in the number of players $n$. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate correlated equilibrium, and no efficient randomized algorithm can reach an exact correlated equilibrium. The results are obtained by bounding from below the number of payoff queries that are needed.

The Query Complexity of Correlated Equilibria

2013-05-21 19:33:32

Sergiu Hart, Noam Nisan

http://dx.doi.org/10.1016/j.geb.2016.11.003, http://arxiv.org/abs/1305.4874v2, http://arxiv.org/pdf/1305.4874v2

cs.GT

th

We consider a model of matching in trading networks in which firms can enter into bilateral contracts. In trading networks, stable outcomes, which are immune to deviations of arbitrary sets of firms, may not exist. We define a new solution concept called trail stability. Trail-stable outcomes are immune to consecutive, pairwise deviations between linked firms. We show that any trading network with bilateral contracts has a trail-stable outcome whenever firms' choice functions satisfy the full substitutability condition. For trail-stable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness, and comparative statics of firm entry and exit. We also introduce weak trail stability which is implied by trail stability under full substitutability. We describe relationships between the solution concepts.

Trading Networks with Bilateral Contracts

2015-10-01 18:03:55

Tamás Fleiner, Zsuzsanna Jankó, Akihisa Tamura, Alexander Teytelboym

http://arxiv.org/abs/1510.01210v3, http://arxiv.org/pdf/1510.01210v3

cs.GT

th

The first ever human vs. computer no-limit Texas hold 'em competition took place from April 24-May 8, 2015 at River's Casino in Pittsburgh, PA. In this article I present my thoughts on the competition design, agent architecture, and lessons learned.

My Reflections on the First Man vs. Machine No-Limit Texas Hold 'em Competition

2015-10-29 09:53:15

Sam Ganzfried

http://arxiv.org/abs/1510.08578v2, http://arxiv.org/pdf/1510.08578v2

cs.GT

th

We study the problem of Bayesian learning in a dynamical system involving strategic agents with asymmetric information. In a series of seminal papers in the literature, this problem has been investigated under a simplifying model where myopically selfish players appear sequentially and act once in the game, based on private noisy observations of the system state and public observation of past players' actions. It has been shown that there exist information cascades where users discard their private information and mimic the action of their predecessor. In this paper, we provide a framework for studying Bayesian learning dynamics in a more general setting than the one described above. In particular, our model incorporates cases where players are non-myopic and strategically participate for the whole duration of the game, and cases where an endogenous process selects which subset of players will act at each time instance. The proposed framework hinges on a sequential decomposition methodology for finding structured perfect Bayesian equilibria (PBE) of a general class of dynamic games with asymmetric information, where user-specific states evolve as conditionally independent Markov processes and users make independent noisy observations of their states. Using this methodology, we study a specific dynamic learning model where players make decisions about public investment based on their estimates of everyone's types. We characterize a set of informational cascades for this problem where learning stops for the team as a whole. We show that in such cascades, all players' estimates of other players' types freeze even though each individual player asymptotically learns its own true type.

Decentralized Bayesian learning in dynamic games: A framework for studying informational cascades

2016-07-23 00:29:18

Deepanshu Vasal, Achilleas Anastasopoulos

http://arxiv.org/abs/1607.06847v2, http://arxiv.org/pdf/1607.06847v2

cs.GT

th

We study a sequential-learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors' actions. They weigh these actions according the strengths of their social connections to different predecessors. We show this rule arises endogenously when agents wrongly believe others act solely on private information and thus neglect redundancies among observations. We provide a simple linear formula expressing agents' actions in terms of network paths and use this formula to characterize the set of networks where naive agents eventually learn correctly. This characterization implies that, on all networks where later agents observe more than one neighbor, there exist disproportionately influential early agents who can cause herding on incorrect actions. Going beyond existing social-learning results, we compute the probability of such mislearning exactly. This allows us to compare likelihoods of incorrect herding, and hence expected welfare losses, across network structures. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups.

Network Structure and Naive Sequential Learning

2017-02-25 09:49:04

Krishna Dasaratha, Kevin He

http://dx.doi.org/10.3982/TE3388, http://arxiv.org/abs/1703.02105v7, http://arxiv.org/pdf/1703.02105v7

q-fin.EC

th

Agents learn about a changing state using private signals and their neighbors' past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbors' estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioral assumption. We examine whether information aggregation is nearly optimal as neighborhoods grow large. A key condition for this is signal diversity: each individual's neighbors have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity $\unicode{x2013}$ e.g., if private signals are i.i.d. $\unicode{x2013}$ learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one's signal quality than to one's number of neighbors, in contrast to standard models with exogenous updating rules.

Learning from Neighbors about a Changing State

2018-01-06 19:14:47

Krishna Dasaratha, Benjamin Golub, Nir Hak

http://dx.doi.org/10.1093/restud/rdac077, http://arxiv.org/abs/1801.02042v8, http://arxiv.org/pdf/1801.02042v8

econ.TH

th

We consider a model of oligopolistic competition in a market with search frictions, in which competing firms with products of unknown quality advertise how much information a consumer's visit will glean. In the unique symmetric equilibrium of this game, the countervailing incentives of attraction and persuasion yield a payoff function for each firm that is linear in the firm's realized effective value. If the expected quality of the products is sufficiently high (or competition is sufficiently fierce), this corresponds to full information--firms provide the first-best level of information. If not, this corresponds to information dispersion--firms randomize over signals.

Attraction versus Persuasion: Information Provision in Search Markets

2018-02-26 18:25:32

Pak Hung Au, Mark Whitmeyer

http://arxiv.org/abs/1802.09396v7, http://arxiv.org/pdf/1802.09396v7

math.PR

th

Melamed, Harrell, and Simpson have recently reported on an experiment which appears to show that cooperation can arise in a dynamic network without reputational knowledge, i.e., purely via dynamics [1]. We believe that their experimental design is actually not testing this, in so far as players do know the last action of their current partners before making a choice on their own next action and subsequently deciding which link to cut. Had the authors given no information at all, the result would be a decline in cooperation as shown in [2].

Reputation is required for cooperation to emerge in dynamic networks

2018-03-16 02:39:21

Jose A. Cuesta, Carlos Gracia-Lázaro, Yamir Moreno, Angel Sánchez

http://arxiv.org/abs/1803.06035v1, http://arxiv.org/pdf/1803.06035v1

physics.soc-ph

th

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the "gambler's fallacy"), they understate the likelihood of consecutive below-average draws, converge to over-pessimistic beliefs about the distribution's mean, and stop too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.

Mislearning from Censored Data: The Gambler's Fallacy and Other Correlational Mistakes in Optimal-Stopping Problems

2018-03-22 02:21:54

Kevin He

http://dx.doi.org/10.3982/TE4657, http://arxiv.org/abs/1803.08170v6, http://arxiv.org/pdf/1803.08170v6

q-fin.EC

th

Currency trading (Forex) is the largest world market in terms of volume. We analyze trading and tweeting about the EUR-USD currency pair over a period of three years. First, a large number of tweets were manually labeled, and a Twitter stance classification model is constructed. The model then classifies all the tweets by the trading stance signal: buy, hold, or sell (EUR vs. USD). The Twitter stance is compared to the actual currency rates by applying the event study methodology, well-known in financial economics. It turns out that there are large differences in Twitter stance distribution and potential trading returns between the four groups of Twitter users: trading robots, spammers, trading companies, and individual traders. Additionally, we observe attempts of reputation manipulation by post festum removal of tweets with poor predictions, and deleting/reposting of identical tweets to increase the visibility without tainting one's Twitter timeline.

Forex trading and Twitter: Spam, bots, and reputation manipulation

2018-04-06 15:36:28

Igor Mozetič, Peter Gabrovšek, Petra Kralj Novak

http://arxiv.org/abs/1804.02233v2, http://arxiv.org/pdf/1804.02233v2

cs.SI

th

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a 3-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all.

Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game

2018-04-13 08:15:28

Sam Ganzfried, Austin Nowak, Joannier Pinales

http://arxiv.org/abs/1804.04789v1, http://arxiv.org/pdf/1804.04789v1

cs.GT

th

We propose a method to design a decentralized energy market which guarantees individual rationality (IR) in expectation, in the presence of system-level grid constraints. We formulate the market as a welfare maximization problem subject to IR constraints, and we make use of Lagrangian duality to model the problem as a n-person non-cooperative game with a unique generalized Nash equilibrium (GNE). We provide a distributed algorithm which converges to the GNE. The convergence and properties of the algorithm are investigated by means of numerical simulations.

A rational decentralized generalized Nash equilibrium seeking for energy markets

2018-06-04 15:33:13

Lorenzo Nespoli, Matteo Salani, Vasco Medici

http://arxiv.org/abs/1806.01072v1, http://arxiv.org/pdf/1806.01072v1

cs.CE

th

We study online pricing algorithms for the Bayesian selection problem with production constraints and its generalization to the laminar matroid Bayesian online selection problem. Consider a firm producing (or receiving) multiple copies of different product types over time. The firm can offer the products to arriving buyers, where each buyer is interested in one product type and has a private valuation drawn independently from a possibly different but known distribution. Our goal is to find an adaptive pricing for serving the buyers that maximizes the expected social-welfare (or revenue) subject to two constraints. First, at any time the total number of sold items of each type is no more than the number of produced items. Second, the total number of sold items does not exceed the total shipping capacity. This problem is a special case of the well-known matroid Bayesian online selection problem studied in [Kleinberg and Weinberg, 2012], when the underlying matroid is laminar. We give the first Polynomial-Time Approximation Scheme (PTAS) for the above problem as well as its generalization to the laminar matroid Bayesian online selection problem when the depth of the laminar family is bounded by a constant. Our approach is based on rounding the solution of a hierarchy of linear programming relaxations that systematically strengthen the commonly used ex-ante linear programming formulation of these problems and approximate the optimum online solution with any degree of accuracy. Our rounding algorithm respects the relaxed constraints of higher-levels of the laminar tree only in expectation, and exploits the negative dependency of the selection rule of lower-levels to achieve the required concentration that guarantees the feasibility with high probability.

Nearly Optimal Pricing Algorithms for Production Constrained and Laminar Bayesian Selection

2018-07-15 05:19:33

Nima Anari, Rad Niazadeh, Amin Saberi, Ali Shameli

http://arxiv.org/abs/1807.05477v1, http://arxiv.org/pdf/1807.05477v1

cs.GT

th

Direct democracy is a special case of an ensemble of classifiers, where every person (classifier) votes on every issue. This fails when the average voter competence (classifier accuracy) falls below 50%, which can happen in noisy settings where voters have only limited information, or when there are multiple topics and the average voter competence may not be high enough for some topics. Representative democracy, where voters choose representatives to vote, can be an elixir in both these situations. Representative democracy is a specific way to improve the ensemble of classifiers. We introduce a mathematical model for studying representative democracy, in particular understanding the parameters of a representative democracy that gives maximum decision making capability. Our main result states that under general and natural conditions, 1. Representative democracy can make the correct decisions simultaneously for multiple noisy issues. 2. When the cost of voting is fixed, the optimal representative democracy requires that representatives are elected from constant sized groups: the number of representatives should be linear in the number of voters. 3. When the cost and benefit of voting are both polynomial, the optimal group size is close to linear in the number of voters. This work sets the mathematical foundation for studying the quality-quantity tradeoff in a representative democracy-type ensemble (fewer highly qualified representatives versus more less qualified representatives).

A Mathematical Model for Optimal Decisions in a Representative Democracy

2018-07-17 03:09:53

Malik Magdon-Ismail, Lirong Xia

http://arxiv.org/abs/1807.06157v1, http://arxiv.org/pdf/1807.06157v1

cs.GT

th

Cooperative behavior in real social dilemmas is often perceived as a phenomenon emerging from norms and punishment. To overcome this paradigm, we highlight the interplay between the influence of social networks on individuals, and the activation of spontaneous self-regulating mechanisms, which may lead them to behave cooperatively, while interacting with others and taking conflicting decisions over time. By extending Evolutionary game theory over networks, we prove that cooperation partially or fully emerges whether self-regulating mechanisms are sufficiently stronger than social pressure. Interestingly, even few cooperative individuals act as catalyzing agents for the cooperation of others, thus activating a recruiting mechanism, eventually driving the whole population to cooperate.

Self-regulation promotes cooperation in social networks

2018-07-20 17:06:43

Dario Madeo, Chiara Mocenni

http://arxiv.org/abs/1807.07848v1, http://arxiv.org/pdf/1807.07848v1

physics.soc-ph

th

This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like coalition-proof Nash equilibrium. Central to this framework is a novel solution concept called cooperative equilibrium system (CES). CES differs from Nash equilibrium in two important respects. First, a CES is immune to both unilateral and multilateral `credible' deviations. Second, unlike Nash equilibrium, whose stability relies on the assumption that the strategies of non-deviating players are held fixed, CES allows for the possibility that players may regroup and adjust their strategies in response to a deviation. The main result establishes that every cooperative extensive form game, possibly with imperfect information, possesses a CES. For games with perfect information, the proof is constructive. This framework is broadly applicable in contexts such as oligopolistic markets and dynamic political bargaining.

The strategy of conflict and cooperation

2018-08-21 06:27:42

Mehmet S. Ismail

http://arxiv.org/abs/1808.06750v7, http://arxiv.org/pdf/1808.06750v7

econ.TH

th

We study a two-stage model, in which students are 1) admitted to college on the basis of an entrance exam which is a noisy signal about their qualifications (type), and then 2) those students who were admitted to college can be hired by an employer as a function of their college grades, which are an independently drawn noisy signal of their type. Students are drawn from one of two populations, which might have different type distributions. We assume that the employer at the end of the pipeline is rational, in the sense that it computes a posterior distribution on student type conditional on all information that it has available (college admissions, grades, and group membership), and makes a decision based on posterior expectation. We then study what kinds of fairness goals can be achieved by the college by setting its admissions rule and grading policy. For example, the college might have the goal of guaranteeing equal opportunity across populations: that the probability of passing through the pipeline and being hired by the employer should be independent of group membership, conditioned on type. Alternately, the college might have the goal of incentivizing the employer to have a group blind hiring rule. We show that both goals can be achieved when the college does not report grades. On the other hand, we show that under reasonable conditions, these goals are impossible to achieve even in isolation when the college uses an (even minimally) informative grading policy.

Downstream Effects of Affirmative Action

2018-08-27 22:15:15

Sampath Kannan, Aaron Roth, Juba Ziani

http://arxiv.org/abs/1808.09004v1, http://arxiv.org/pdf/1808.09004v1

cs.GT

th

We map the recently proposed notions of algorithmic fairness to economic models of Equality of opportunity (EOP)---an extensively studied ideal of fairness in political philosophy. We formally show that through our conceptual mapping, many existing definition of algorithmic fairness, such as predictive value parity and equality of odds, can be interpreted as special cases of EOP. In this respect, our work serves as a unifying moral framework for understanding existing notions of algorithmic fairness. Most importantly, this framework allows us to explicitly spell out the moral assumptions underlying each notion of fairness, and interpret recent fairness impossibility results in a new light. Last but not least and inspired by luck egalitarian models of EOP, we propose a new family of measures for algorithmic fairness. We illustrate our proposal empirically and show that employing a measure of algorithmic (un)fairness when its underlying moral assumptions are not satisfied, can have devastating consequences for the disadvantaged group's welfare.

A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity

2018-09-10 18:33:51

Hoda Heidari, Michele Loi, Krishna P. Gummadi, Andreas Krause

http://arxiv.org/abs/1809.03400v2, http://arxiv.org/pdf/1809.03400v2

cs.LG

th

In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that influence the decisions of the players. The current theory for correlated games, however, enforces the players to obey the instructions from a third party or "correlation device" to reach equilibrium, but this cannot be achieved for all initial correlations. We extend here the existing framework of correlated games and find that there are other interesting and previously unknown Nash equilibria that make use of correlations to obtain the best payoff. This is achieved by allowing the players the freedom to follow or not to follow the suggestions of the correlation device. By assigning independent probabilities to follow every possible suggestion, the players engage in a response game that turns out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and mixed-strategy solutions. We determine the Nash equilibria for all possible correlated Snowdrift games, which we find to be describable by Ising Models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.

Nash Equilibria in the Response Strategy of Correlated Games

2018-09-07 15:52:12

A. D. Correia, H. T. C. Stoof

http://dx.doi.org/10.1038/s41598-018-36562-2, http://arxiv.org/abs/1809.03860v1, http://arxiv.org/pdf/1809.03860v1

physics.soc-ph

th

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditional optimal mechanism design approach is ill-suited---either because it makes overly strong assumptions, or because it advocates overly complex designs. This survey reviews several common issues with optimal mechanisms, including exorbitant communication, computation, and informational requirements; and it presents several examples demonstrating that passing to the relaxed goal of an approximately optimal mechanism allows us to reason about fundamental questions that seem out of reach of the traditional theory.

Approximately Optimal Mechanism Design

2018-12-31 19:54:47

Tim Roughgarden, Inbal Talgam-Cohen

http://arxiv.org/abs/1812.11896v2, http://arxiv.org/pdf/1812.11896v2

econ.TH

th

This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time, uncertainty and fuzziness. Related to time preference, it is noted that the subadditive discounting is mandatory in positive rewards situations and, consequently, results in the magnitude effect and time effect, where the last has a stronger discounting for earlier delay periods (as in, one hour, one day), but a weaker discounting for longer delay periods (for instance, six months, one year, ten years). In addition, it is possible to explain the preference reversal (change of preference when two rewards proposed on different dates are shifted in the time). Related to the Prospect Theory, it is shown that the risk seeking and the risk aversion are magnitude dependents, where the risk seeking may disappear when the values to be lost are very high.

Decision-making and Fuzzy Temporal Logic

2019-01-07 21:56:24

José Cláudio do Nascimento

http://arxiv.org/abs/1901.01970v2, http://arxiv.org/pdf/1901.01970v2

cs.AI

th

As financial instruments grow in complexity more and more information is neglected by risk optimization practices. This brings down a curtain of opacity on the origination of risk, that has been one of the main culprits in the 2007-2008 global financial crisis. We discuss how the loss of transparency may be quantified in bits, using information theoretic concepts. We find that {\em i)} financial transformations imply large information losses, {\em ii)} portfolios are more information sensitive than individual stocks only if fundamental analysis is sufficiently informative on the co-movement of assets, that {\em iii)} securitisation, in the relevant range of parameters, yields assets that are less information sensitive than the original stocks and that {\em iv)} when diversification (or securitisation) is at its best (i.e. when assets are uncorrelated) information losses are maximal. We also address the issue of whether pricing schemes can be introduced to deal with information losses. This is relevant for the transmission of incentives to gather information on the risk origination side. Within a simple mean variance scheme, we find that market incentives are not generally sufficient to make information harvesting sustainable.

Lost in Diversification

2019-01-28 19:39:51

Marco Bardoscia, Daniele d'Arienzo, Matteo Marsili, Valerio Volpati

http://dx.doi.org/10.1016/j.crhy.2019.05.015, http://arxiv.org/abs/1901.09795v1, http://arxiv.org/pdf/1901.09795v1

q-fin.GN

th

The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been popularized in the recent literature. MFE takes advantage of averaging effects in models with a large number of players. We make three main contributions. First, our main result provides conditions that ensure the uniqueness of an MFE. We believe this uniqueness result is the first of its nature in the class of models we study. Second, we generalize previous MFE existence results. Third, we provide general comparative statics results. We apply our results to dynamic oligopoly models and to heterogeneous agent macroeconomic models commonly used in previous work in economics and operations.

Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

2019-03-06 12:56:58

Bar Light, Gabriel Weintraub

http://arxiv.org/abs/1903.02273v3, http://arxiv.org/pdf/1903.02273v3

econ.TH

th

We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games which generalize wars of attrition. Previously known examples of variable concession games in the literature yield equilibria characterized by singular control strategies without any delay of concession. However, these no-delay equilibria are in contrast to mixed strategy equilibria of canonical wars of attrition in which each player delays concession by a randomized time. We find that a variable contribution game with a single state variable, which extends the Nerlove-Arrow model, possesses an equilibrium characterized by regular control strategies that result in a gradual concession. This equilibrium naturally generalizes the mixed strategy equilibria from the canonical wars of attrition. Stochasticity of the problem accentuates the qualitative difference between a singular control solution and a regular control equilibrium solution. We also find that asymmetry between the players can mitigate the inefficiency caused by the gradualism.

Game of Variable Contributions to the Common Good under Uncertainty

2019-04-01 01:41:25

H. Dharma Kwon

http://dx.doi.org/10.1287/opre.2019.1879, http://arxiv.org/abs/1904.00500v1, http://arxiv.org/pdf/1904.00500v1

math.OC

th

Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach and find an impossibility theorem: any self-consistent ranking method, which satisfies a natural monotonicity property, should depend on the level of aggregation. Our result presents a trade-off between two axiomatic properties and reveals a dilemma of aggregation.

Journal ranking should depend on the level of aggregation

2019-04-08 16:27:34

László Csató

http://dx.doi.org/10.1016/j.joi.2019.100975, http://arxiv.org/abs/1904.06300v4, http://arxiv.org/pdf/1904.06300v4

cs.DL

th

We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning ability to interpret news or private information in time-varying networks. Under general assumption on the noise, a limit theorem is developed for the generalised DeGroot framework for certain type of conditions governing the learning. In this context, the agents beliefs (properly scaled) converge in distribution that is not necessarily normal. Fresh insights are gained not only from proposing a new setting for social learning models but also from using different techniques to study discrete time random linear dynamical systems.

Averaging plus Learning Models and Their Asymptotics

2019-04-17 11:34:14

Ionel Popescu, Tushar Vaidya

http://dx.doi.org/10.1098/rspa.2022.0681, http://arxiv.org/abs/1904.08131v5, http://arxiv.org/pdf/1904.08131v5

q-fin.MF

th

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. Current literature has characterized asymptotic behavior under fairly specific assumptions. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a generalization of a differential equation that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.

Asymptotic Behavior of Bayesian Learners with Misspecified Models

2019-04-18 03:58:32

Ignacio Esponda, Demian Pouzo, Yuichi Yamamoto

http://arxiv.org/abs/1904.08551v2, http://arxiv.org/pdf/1904.08551v2

econ.TH

th

The literature specifies extensive-form games in many styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines $\mathbf{NCF}$, the category of node-and-choice forms. The category's objects are extensive forms in essentially any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. Further, this paper develops two full subcategories: $\mathbf{CsqF}$ for forms whose nodes are choice-sequences, and $\mathbf{CsetF}$ for forms whose nodes are choice-sets. I show that $\mathbf{NCF}$ is "isomorphically enclosed" in $\mathbf{CsqF}$ in the sense that each $\mathbf{NCF}$ form is isomorphic to a $\mathbf{CsqF}$ form. Similarly, I show that $\mathbf{CsqF_{\tilde a}}$ is isomorphically enclosed in $\mathbf{CsetF}$ in the sense that each $\mathbf{CsqF}$ form with no-absentmindedness is isomorphic to a $\mathbf{CsetF}$ form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz 2016 and Streufert 2019. Aside from the larger agenda, this paper already makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced.

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

2019-04-27 04:30:55

Peter A. Streufert

http://dx.doi.org/10.1007/978-981-15-1342-8_2, http://arxiv.org/abs/1904.12085v1, http://arxiv.org/pdf/1904.12085v1

econ.TH

th

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Renyi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Renyi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Renyi divergences.

From Blackwell Dominance in Large Samples to Renyi Divergences and Back Again

2019-06-07 02:15:02

Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz

http://arxiv.org/abs/1906.02838v5, http://arxiv.org/pdf/1906.02838v5

math.ST

th

With vast databases at their disposal, private tech companies can compete with public statistical agencies to provide population statistics. However, private companies face different incentives to provide high-quality statistics and to protect the privacy of the people whose data are used. When both privacy protection and statistical accuracy are public goods, private providers tend to produce at least one suboptimally, but it is not clear which. We model a firm that publishes statistics under a guarantee of differential privacy. We prove that provision by the private firm results in inefficiently low data quality in this framework.

Suboptimal Provision of Privacy and Statistical Accuracy When They are Public Goods

2019-06-22 02:42:46

John M. Abowd, Ian M. Schmutte, William Sexton, Lars Vilhuber

http://arxiv.org/abs/1906.09353v1, http://arxiv.org/pdf/1906.09353v1

econ.TH

th

Poker is a large complex game of imperfect information, which has been singled out as a major AI challenge problem. Recently there has been a series of breakthroughs culminating in agents that have successfully defeated the strongest human players in two-player no-limit Texas hold 'em. The strongest agents are based on algorithms for approximating Nash equilibrium strategies, which are stored in massive binary files and unintelligible to humans. A recent line of research has explored approaches for extrapolating knowledge from strong game-theoretic strategies that can be understood by humans. This would be useful when humans are the ultimate decision maker and allow humans to make better decisions from massive algorithmically-generated strategies. Using techniques from machine learning we have uncovered a new simple, fundamental rule of poker strategy that leads to a significant improvement in performance over the best prior rule and can also easily be applied by human players.

Most Important Fundamental Rule of Poker Strategy

2019-06-09 01:42:24

Sam Ganzfried, Max Chiswick

http://arxiv.org/abs/1906.09895v3, http://arxiv.org/pdf/1906.09895v3

cs.AI

th

We propose new Degroot-type social learning models with feedback in a continuous time, to investigate the effect of a noisy information source on consensus formation in a social network. Unlike the standard Degroot framework, noisy information models destroy consensus formation. On the other hand, the noisy opinion dynamics converge to the equilibrium distribution that encapsulates correlations among agents' opinions. Interestingly, such an equilibrium distribution is also a non-equilibrium steady state (NESS) with a non-zero probabilistic current loop. Thus, noisy information source leads to a NESS at long times that encodes persistent correlated opinion dynamics of learning agents. Our model provides a simple realization of NESS in the context of social learning. Other phenomena such as synchronization of opinions when agents are subject to a common noise are also studied.

Broken Detailed Balance and Non-Equilibrium Dynamics in Noisy Social Learning Models

2019-06-27 11:00:36

Tushar Vaidya, Thiparat Chotibut, Georgios Piliouras

http://dx.doi.org/10.1016/j.physa.2021.125818, http://arxiv.org/abs/1906.11481v2, http://arxiv.org/pdf/1906.11481v2

physics.soc-ph

th

We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities when monetary transfers are not allowed. The competitive rule is known for its remarkable fairness and efficiency properties in the case of goods. This rule was extended to chores in prior work by Bogomolnaia, Moulin, Sandomirskiy, and Yanovskaya (2017). The rule produces Pareto optimal and envy-free allocations for both goods and chores. In the case of goods, the outcome of the competitive rule can be easily computed. Competitive allocations solve the Eisenberg-Gale convex program; hence the outcome is unique and can be approximately found by standard gradient methods. An exact algorithm that runs in polynomial time in the number of agents and goods was given by Orlin (2010). In the case of chores, the competitive rule does not solve any convex optimization problem; instead, competitive allocations correspond to local minima, local maxima, and saddle points of the Nash social welfare on the Pareto frontier of the set of feasible utilities. The Pareto frontier may contain many such points; consequently, the competitive rule's outcome is no longer unique. In this paper, we show that all the outcomes of the competitive rule for chores can be computed in strongly polynomial time if either the number of agents or the number of chores is fixed. The approach is based on a combination of three ideas: all consumption graphs of Pareto optimal allocations can be listed in polynomial time; for a given consumption graph, a candidate for a competitive utility profile can be constructed via an explicit formula; each candidate can be checked for competitiveness, and the allocation can be reconstructed using a maximum flow computation. Our algorithm gives an approximately-fair allocation of indivisible chores by the rounding technique of Barman and Krishnamurthy (2018).

Algorithms for Competitive Division of Chores

2019-07-03 09:55:04

Simina Brânzei, Fedor Sandomirskiy

http://arxiv.org/abs/1907.01766v2, http://arxiv.org/pdf/1907.01766v2

cs.GT

th

We study a model of vendors competing to sell a homogeneous product to customers spread evenly along a linear city. This model is based on Hotelling's celebrated paper in 1929. Our aim in this paper is to present a necessary and sufficient condition for the equilibrium. This yields a representation for the equilibrium. To achieve this, we first formulate the model mathematically. Next, we prove that the condition holds if and only if vendors are equilibrium.

Necessary and sufficient condition for equilibrium of the Hotelling model

2019-07-14 13:26:40

Satoshi Hayashi, Naoki Tsuge

http://arxiv.org/abs/1907.06200v1, http://arxiv.org/pdf/1907.06200v1

econ.TH

th

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short lived recessions; alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, {\it narratives} become an important monetary policy tool, that can help steering the economy back on track.

Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model

2019-07-17 13:13:35

Federico Guglielmo Morelli, Michael Benzaquen, Marco Tarzia, Jean-Philippe Bouchaud

http://arxiv.org/abs/1907.07425v1, http://arxiv.org/pdf/1907.07425v1

q-fin.GN

th

How does supply uncertainty affect the structure of supply chain networks? To answer this question we consider a setting where retailers and suppliers must establish a costly relationship with each other prior to engaging in trade. Suppliers, with uncertain yield, announce wholesale prices, while retailers must decide which suppliers to link to based on their wholesale prices. Subsequently, retailers compete with each other in Cournot fashion to sell the acquired supply to consumers. We find that in equilibrium retailers concentrate their links among too few suppliers, i.e., there is insufficient diversification of the supply base. We find that either reduction of supply variance or increase of mean supply, increases a supplier's profit. However, these two ways of improving service have qualitatively different effects on welfare: improvement of the expected supply by a supplier makes everyone better off, whereas improvement of supply variance lowers consumer surplus.

Yield Uncertainty and Strategic Formation of Supply Chain Networks

2019-07-20 19:19:46

Victor Amelkin, Rakesh Vohra

http://dx.doi.org/10.1002/net.22186, http://arxiv.org/abs/1907.09943v1, http://arxiv.org/pdf/1907.09943v1

cs.GT

th

Motivated by the problem of market power in electricity markets, we introduced in previous works a mechanism for simplified markets of two agents with linear cost. In standard procurement auctions, the market power resulting from the quadratic transmission losses allows the producers to bid above their true values, which are their production cost. The mechanism proposed in the previous paper optimally reduces the producers' margin to the society's benefit. In this paper, we extend those results to a more general market made of a finite number of agents with piecewise linear cost functions, which makes the problem more difficult, but simultaneously more realistic. We show that the methodology works for a large class of externalities. We also provide an algorithm to solve the principal allocation problem. Our contribution provides a benchmark to assess the sub-optimality of the mechanisms used in practice.

Optimal auctions for networked markets with externalities

2019-07-23 21:02:28

Benjamin Heymann, Alejandro Jofré

http://arxiv.org/abs/1907.10080v1, http://arxiv.org/pdf/1907.10080v1

econ.TH

th

Exchanges acquire excess processing capacity to accommodate trading activity surges associated with zero-sum high-frequency trader (HFT) "duels." The idle capacity's opportunity cost is an externality of low-latency trading. We build a model of decentralized exchanges (DEX) with flexible capacity. On DEX, HFTs acquire speed in real-time from peer-to-peer networks. The price of speed surges during activity bursts, as HFTs simultaneously race to market. Relative to centralized exchanges, HFTs acquire more speed on DEX, but for shorter timespans. Low-latency "sprints" speed up price discovery without harming liquidity. Overall, speed rents decrease and fewer resources are locked-in to support zero-sum HFT trades.

Liquid Speed: On-Demand Fast Trading at Distributed Exchanges

2019-07-24 23:56:12

Michael Brolley, Marius Zoican

http://arxiv.org/abs/1907.10720v1, http://arxiv.org/pdf/1907.10720v1

q-fin.TR

th

The stochastic multi-armed bandit model captures the tradeoff between exploration and exploitation. We study the effects of competition and cooperation on this tradeoff. Suppose there are $k$ arms and two players, Alice and Bob. In every round, each player pulls an arm, receives the resulting reward, and observes the choice of the other player but not their reward. Alice's utility is $\Gamma_A + \lambda \Gamma_B$ (and similarly for Bob), where $\Gamma_A$ is Alice's total reward and $\lambda \in [-1, 1]$ is a cooperation parameter. At $\lambda = -1$ the players are competing in a zero-sum game, at $\lambda = 1$, they are fully cooperating, and at $\lambda = 0$, they are neutral: each player's utility is their own reward. The model is related to the economics literature on strategic experimentation, where usually players observe each other's rewards. With discount factor $\beta$, the Gittins index reduces the one-player problem to the comparison between a risky arm, with a prior $\mu$, and a predictable arm, with success probability $p$. The value of $p$ where the player is indifferent between the arms is the Gittins index $g = g(\mu,\beta) > m$, where $m$ is the mean of the risky arm. We show that competing players explore less than a single player: there is $p^* \in (m, g)$ so that for all $p > p^*$, the players stay at the predictable arm. However, the players are not myopic: they still explore for some $p > m$. On the other hand, cooperating players explore more than a single player. We also show that neutral players learn from each other, receiving strictly higher total rewards than they would playing alone, for all $ p\in (p^*, g)$, where $p^*$ is the threshold from the competing case. Finally, we show that competing and neutral players eventually settle on the same arm in every Nash equilibrium, while this can fail for cooperating players.

Multiplayer Bandit Learning, from Competition to Cooperation

2019-08-03 11:20:54

Simina Brânzei, Yuval Peres

http://arxiv.org/abs/1908.01135v3, http://arxiv.org/pdf/1908.01135v3

cs.GT

th

We outline a token model for Truebit, a retrofitting, blockchain enhancement which enables secure, community-based computation. The model addresses the challenge of stable task pricing, as raised in the Truebit whitepaper, without appealing to external oracles, exchanges, or hierarchical nodes. The system's sustainable economics and fair market pricing derive from a mintable token format which leverages existing tokens for liquidity. Finally, we introduce a governance layer whose lifecycles culminates with permanent dissolution into utility tokens, thereby tending the network towards autonomous decentralization.

Bootstrapping a stable computation token

2019-08-08 09:41:13

Jason Teutsch, Sami Mäkelä, Surya Bakshi

http://arxiv.org/abs/1908.02946v1, http://arxiv.org/pdf/1908.02946v1

cs.CR

th

In December 2015, a bounty emerged to establish both reliable communication and secure transfer of value between the Dogecoin and Ethereum blockchains. This prized "Dogethereum bridge" would allow parties to "lock" a DOGE coin on Dogecoin and in exchange receive a newly minted WOW token in Ethereum. Any subsequent owner of the WOW token could burn it and, in exchange, earn the right to "unlock" a DOGE on Dogecoin. We describe an efficient, trustless, and retrofitting Dogethereum construction which requires no fork but rather employs economic collateral to achieve a "lock" operation in Dogecoin. The protocol relies on bulletproofs, Truebit, and parametrized tokens to efficiently and trustlessly relay events from the "true" Dogecoin blockchain into Ethereum. The present construction not only enables cross-platform exchange but also allows Ethereum smart contracts to trustlessly access Dogecoin. A similar technique adds Ethereum-based smart contracts to Bitcoin and Bitcoin data to Ethereum smart contracts.

Retrofitting a two-way peg between blockchains

2019-08-12 07:41:13

Jason Teutsch, Michael Straka, Dan Boneh

http://arxiv.org/abs/1908.03999v1, http://arxiv.org/pdf/1908.03999v1

cs.CR

th

Ethereum has emerged as a dynamic platform for exchanging cryptocurrency tokens. While token crowdsales cannot simultaneously guarantee buyers both certainty of valuation and certainty of participation, we show that if each token buyer specifies a desired purchase quantity at each valuation then everyone can successfully participate. Our implementation introduces smart contract techniques which recruit outside participants in order to circumvent computational complexity barriers.

Interactive coin offerings

2019-08-12 07:30:55

Jason Teutsch, Vitalik Buterin, Christopher Brown

http://arxiv.org/abs/1908.04295v1, http://arxiv.org/pdf/1908.04295v1

econ.TH

th

We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile. The analysis ultimately boils down to thinking about positional voting systems in terms of doubly stochastic matrices.

Positional Voting and Doubly Stochastic Matrices

2019-08-18 22:48:33

Jacqueline Anderson, Brian Camara, John Pike

http://arxiv.org/abs/1908.06506v2, http://arxiv.org/pdf/1908.06506v2

math.CO

th

For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We consider pure and mixed stopping strategies and a (subgame perfect Nash) equilibrium. We provide different necessary and sufficient equilibrium conditions including a verification theorem. Using a fixed point argument we provide equilibrium existence results. We adapt and study the notion of the myopic adjustment process and introduce different kinds of equilibrium stability. We show that neither existence nor uniqueness of equilibria should generally be expected. The developed theory is applied to a mean-variance problem and a variance problem.

Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application

2019-09-26 09:17:03

Sören Christensen, Kristoffer Lindensjö

http://arxiv.org/abs/1909.11921v2, http://arxiv.org/pdf/1909.11921v2

math.OC

th

The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [16] showing that it is the \emph{unique} method that satisfies certain good properties (\emph{axioms}). There are, however, a multiplicity of ways in which the Shapley value is operationalized in the attribution problem. These differ in how they reference the model, the training data, and the explanation context. These give very different results, rendering the uniqueness result meaningless. Furthermore, we find that previously proposed approaches can produce counterintuitive attributions in theory and in practice---for instance, they can assign non-zero attributions to features that are not even referenced by the model. In this paper, we use the axiomatic approach to study the differences between some of the many operationalizations of the Shapley value for attribution, and propose a technique called Baseline Shapley (BShap) that is backed by a proper uniqueness result. We also contrast BShap with Integrated Gradients, another extension of Shapley value to the continuous setting.

The many Shapley values for model explanation

2019-08-22 19:13:10

Mukund Sundararajan, Amir Najmi

http://arxiv.org/abs/1908.08474v2, http://arxiv.org/pdf/1908.08474v2

cs.AI

th

In this article we solve the problem of maximizing the expected utility of future consumption and terminal wealth to determine the optimal pension or life-cycle fund strategy for a cohort of pension fund investors. The setup is strongly related to a DC pension plan where additionally (individual) consumption is taken into account. The consumption rate is subject to a time-varying minimum level and terminal wealth is subject to a terminal floor. Moreover, the preference between consumption and terminal wealth as well as the intertemporal coefficient of risk aversion are time-varying and therefore depend on the age of the considered pension cohort. The optimal consumption and investment policies are calculated in the case of a Black-Scholes financial market framework and hyperbolic absolute risk aversion (HARA) utility functions. We generalize Ye (2008) (2008 American Control Conference, 356-362) by adding an age-dependent coefficient of risk aversion and extend Steffensen (2011) (Journal of Economic Dynamics and Control, 35(5), 659-667), Hentschel (2016) (Doctoral dissertation, Ulm University) and Aase (2017) (Stochastics, 89(1), 115-141) by considering consumption in combination with terminal wealth and allowing for consumption and terminal wealth floors via an application of HARA utility functions. A case study on fitting several models to realistic, time-dependent life-cycle consumption and relative investment profiles shows that only our extended model with time-varying preference parameters provides sufficient flexibility for an adequate fit. This is of particular interest to life-cycle products for (private) pension investments or pension insurance in general.

Optimal life-cycle consumption and investment decisions under age-dependent risk preferences

2019-08-27 04:17:52

Andreas Lichtenstern, Pavel V. Shevchenko, Rudi Zagst

http://dx.doi.org/10.1007/s11579-020-00276-9, http://arxiv.org/abs/1908.09976v1, http://arxiv.org/pdf/1908.09976v1

q-fin.MF

th

Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies) adopted by individuals in a finite population based on the interactions among them with an eye to modelling behaviour using the following metrics: cost of investment, cost of management, cost of treatment, reputation benefit for the provider(s), and the gained health benefit for the patient.

Modelling Cooperation in a Dynamic Healthcare System

2019-09-06 20:23:39

Zainab Alalawi, Yifeng Zeng, The Anh Han, Aiman Elragig

http://arxiv.org/abs/1909.03070v1, http://arxiv.org/pdf/1909.03070v1

cs.GT

th

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where envy can be eliminated by removing an item from the envied agent's bundle, and weak, where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agent's bundle in the envying agent's bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.

Weighted Envy-Freeness in Indivisible Item Allocation

2019-09-23 20:44:59

Mithun Chakraborty, Ayumi Igarashi, Warut Suksompong, Yair Zick

http://dx.doi.org/10.1145/3457166, http://arxiv.org/abs/1909.10502v7, http://arxiv.org/pdf/1909.10502v7

cs.AI

th

This paper studies dynamic mechanism design in a quasilinear Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent's private information, referred to as state, evolves over time. The agent makes decisions of whether to stop or continue and what to report at each period. The principal, on the other hand, chooses decision rules consisting of an allocation rule and a set of payment rules to maximize her ex-ante expected payoff. In order to influence the agent's stopping decision, one of the terminal payment rules is posted-price, i.e., it depends only on the realized stopping time of the agent. We define the incentive compatibility in this dynamic environment in terms of Bellman equations, which is then simplified by establishing a one-shot deviation principle. Given the optimality of the stopping rule, a sufficient condition for incentive compatibility is obtained by constructing the state-dependent payment rules in terms of a set of functions parameterized by the allocation rule. A necessary condition is derived from envelope theorem, which explicitly formulates the state-dependent payment rules in terms of allocation rules. A class of monotone environment is considered to characterize the optimal stopping by a threshold rule. The posted-price payment rules are then pinned down in terms of the allocation rule and the threshold function up to a constant. The incentive compatibility constraints restrict the design of the posted-price payment rule by a regular condition.

On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment

2019-09-30 17:05:50

Tao Zhang, Quanyan Zhu

http://arxiv.org/abs/1909.13720v4, http://arxiv.org/pdf/1909.13720v4

math.DS

th

We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to lotteries, initial play in games, and human generation of random sequences. We discover considerable variation in the completeness of existing models, which sheds light on whether to focus on developing better models with the same features or instead to look for new features that will improve predictions. We also illustrate how and why completeness varies with the experiments considered, which highlights the role played in choosing which experiments to run.

Measuring the Completeness of Theories

2019-10-15 22:46:54

Drew Fudenberg, Jon Kleinberg, Annie Liang, Sendhil Mullainathan

http://arxiv.org/abs/1910.07022v1, http://arxiv.org/pdf/1910.07022v1

econ.TH

th

This survey explores the literature on game-theoretic models of network formation under the hypothesis of mutual consent in link formation. The introduction of consent in link formation imposes a coordination problem in the network formation process. This survey explores the conclusions from this theory and the various methodologies to avoid the main pitfalls. The main insight originates from Myerson's work on mutual consent in link formation and his main conclusion that the empty network (the network without any links) always emerges as a strong Nash equilibrium in any game-theoretic model of network formation under mutual consent and positive link formation costs. Jackson and Wolinsky introduced a cooperative framework to avoid this main pitfall. They devised the notion of a pairwise stable network to arrive at equilibrium networks that are mainly non-trivial. Unfortunately, this notion of pairwise stability requires coordinated action by pairs of decision makers in link formation. I survey the possible solutions in a purely non-cooperative framework of network formation under mutual consent by exploring potential refinements of the standard Nash equilibrium concept to explain the emergence of non-trivial networks. This includes the notions of unilateral and monadic stability. The first one is founded on advanced rational reasoning of individuals about how others would respond to one's efforts to modify the network. The latter incorporates trusting, boundedly rational behaviour into the network formation process. The survey is concluded with an initial exploration of external correlation devices as an alternative framework to address mutual consent in network formation.

Building social networks under consent: A survey

2019-10-25 16:04:55

Robert P. Gilles

http://arxiv.org/abs/1910.11693v2, http://arxiv.org/pdf/1910.11693v2

econ.TH

th

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this work, we derive mean field game partial differential equation systems from deterministic microscopic agent dynamics. The dynamics are given by a particular class of ordinary differential equations, for which an optimal strategy can be computed (Bressan, Milan Journal of Mathematics, 2011). We use the concept of Nash equilibria and apply the dynamic programming principle to derive the mean field limit equations and we study the scaling behavior of the system as the number of agents tends to infinity and find several mean field game limits. Especially we avoid in our derivation the notion of measure derivatives. Novel scales are motivated by an example of an agent-based financial market model.

Microscopic Derivation of Mean Field Game Models

2019-10-30 00:12:16

Martin Frank, Michael Herty, Torsten Trimborn

http://arxiv.org/abs/1910.13534v1, http://arxiv.org/pdf/1910.13534v1

math.OC

th

The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and biology to economics. Many experimental results of the RPS game indicate that this game is better modelled by the discretized best-response dynamics rather than continuous time dynamics. In this work we show that the attractor of the discrete time best-response dynamics of the RPS game is finite and periodic. Moreover we also describe the bifurcations of the attractor and determine the exact number, period and location of the periodic strategies.

Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game

2019-12-14 15:20:12

José Pedro Gaivão, Telmo Peixe

http://dx.doi.org/10.1007/s13235-020-00371-y, http://arxiv.org/abs/1912.06831v1, http://arxiv.org/pdf/1912.06831v1

math.DS

th

For object reallocation problems, if preferences are strict but otherwise unrestricted, the Top Trading Cycles rule (TTC) is the leading rule: It is the only rule satisfying efficiency, individual rationality, and strategy-proofness. However, on the subdomain of single-peaked preferences, Bade (2019) defines a new rule, the "crawler", which also satisfies these three properties. (i) The crawler selects an allocation by "visiting" agents in a specific order. A natural "dual" rule can be defined by proceeding in the reverse order. Our first theorem states that the crawler and its dual are actually the same. (ii) Single-peakedness of a preference profile may in fact hold for more than one order and its reverse. Our second theorem states that the crawler is invariant to the choice of the order. (iii) For object allocation problems (as opposed to reallocation problems), we define a probabilistic version of the crawler by choosing an endowment profile at random according to a uniform distribution, and applying the original definition. Our third theorem states that this rule is the same as the "random priority rule".

The Crawler: Three Equivalence Results for Object (Re)allocation Problems when Preferences Are Single-peaked

2019-12-14 22:27:12

Yuki Tamura, Hadi Hosseini

http://arxiv.org/abs/1912.06909v2, http://arxiv.org/pdf/1912.06909v2

econ.TH

th

In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (possibly overlapping) types and (2) hospital-doctor matching where various regional quotas are imposed. In this paper, we present a polynomial-time reduction to transform an instance of (1) to an instance of (2) and we show how the feasibility and stability of corresponding matchings are preserved under the reduction. Our reduction provides a formal connection between two important strands of work on matching with distributional constraints. We then apply the reduction in two ways. Firstly, we show that it is NP-complete to check whether a feasible and stable outcome for (1) exists. Due to our reduction, these NP-completeness results carry over to setting (2). In view of this, we help unify some of the results that have been presented in the literature. Secondly, if we have positive results for (2), then we have corresponding results for (1). One key conclusion of our results is that further developments on axiomatic and algorithmic aspects of hospital-doctor matching with regional quotas will result in corresponding results for school choice with diversity constraints.

From Matching with Diversity Constraints to Matching with Regional Quotas

2020-02-17 05:51:46

Haris Aziz, Serge Gaspers, Zhaohong Sun, Toby Walsh

http://arxiv.org/abs/2002.06748v1, http://arxiv.org/pdf/2002.06748v1

cs.GT

th

In a second-price auction with i.i.d. (independent identically distributed) bidder valuations, adding bidders increases expected buyer surplus if the distribution of valuations has a sufficiently heavy right tail. While this does not imply that a bidder in an auction should prefer for more bidders to join the auction, it does imply that a bidder should prefer it in exchange for the bidder being allowed to participate in more auctions. Also, for a heavy-tailed valuation distribution, marginal expected seller revenue per added bidder remains strong even when there are already many bidders.

Heavy Tails Make Happy Buyers

2020-02-20 23:47:42

Eric Bax

http://arxiv.org/abs/2002.09014v1, http://arxiv.org/pdf/2002.09014v1

cs.GT

th

A Euclidean path integral is used to find an optimal strategy for a firm under a Walrasian system, Pareto optimality and a non-cooperative feedback Nash Equilibrium. We define dynamic optimal strategies and develop a Feynman type path integration method to capture all non-additive convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, under Walrasian system we are able to solve for the optimal strategy under a linear constraint with a linear objective function with respect to strategy.

Optimization of a Dynamic Profit Function using Euclidean Path Integral

2020-02-21 19:22:48

P. Pramanik, A. M. Polansky

http://arxiv.org/abs/2002.09394v1, http://arxiv.org/pdf/2002.09394v1

econ.TH

th

A well-known axiom for proportional representation is Proportionality of Solid Coalitions (PSC). We characterize committees satisfying PSC as possible outcomes of the Minimal Demand rule, which generalizes an approach pioneered by Michael Dummett.

A characterization of proportionally representative committees

2020-02-22 04:48:56

Haris Aziz, Barton E. Lee

http://arxiv.org/abs/2002.09598v2, http://arxiv.org/pdf/2002.09598v2

cs.GT

th

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of Aumann's Agreement Theorem, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995). For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

Feasible Joint Posterior Beliefs

2020-02-26 12:01:10

Itai Arieli, Yakov Babichenko, Fedor Sandomirskiy, Omer Tamuz

http://arxiv.org/abs/2002.11362v4, http://arxiv.org/pdf/2002.11362v4

econ.TH

th

We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation is cast within the framework of a controlled non-Markovian forward stochastic differential equation, and a general objective functional setting. We adopt a game-theoretic approach to study such problems, meaning that we seek for sub-game perfect Nash equilibrium points. As a first novelty of this work, we introduce and motivate a refinement of the definition of equilibrium that allows us to establish a direct and rigorous proof of an extended dynamic programming principle, in the same spirit as in the classical theory. This in turn allows us to introduce a system consisting of an infinite family of backward stochastic differential equations analogous to the classical HJB equation. We prove that this system is fundamental, in the sense that its well-posedness is both necessary and sufficient to characterise the value function and equilibria. As a final step we provide an existence and uniqueness result. Some examples and extensions of our results are also presented.

Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents

2020-02-28 09:54:54

Camilo Hernández, Dylan Possamaï

http://arxiv.org/abs/2002.12572v2, http://arxiv.org/pdf/2002.12572v2

math.OC

th

In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider a setting where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2021), for the Pandora's Box problem, which is a classical model for sequential consumer search.

Learning Utilities and Equilibria in Non-Truthful Auctions

2020-07-03 17:44:33

Hu Fu, Tao Lin

http://arxiv.org/abs/2007.01722v3, http://arxiv.org/pdf/2007.01722v3

cs.GT

th

The prisoner's dilemma (PD) is a game-theoretic model studied in a wide array of fields to understand the emergence of cooperation between rational self-interested agents. In this work, we formulate a spatial iterated PD as a discrete-event dynamical system where agents play the game in each time-step and analyse it algebraically using Krohn-Rhodes algebraic automata theory using a computational implementation of the holonomy decomposition of transformation semigroups. In each iteration all players adopt the most profitable strategy in their immediate neighbourhood. Perturbations resetting the strategy of a given player provide additional generating events for the dynamics. Our initial study shows that the algebraic structure, including how natural subsystems comprising permutation groups acting on the spatial distributions of strategies, arise in certain parameter regimes for the pay-off matrix, and are absent for other parameter regimes. Differences in the number of group levels in the holonomy decomposition (an upper bound for Krohn-Rhodes complexity) are revealed as more pools of reversibility appear when the temptation to defect is at an intermediate level. Algebraic structure uncovered by this analysis can be interpreted to shed light on the dynamics of the spatial iterated PD.

Spatial Iterated Prisoner's Dilemma as a Transformation Semigroup

2020-07-03 21:20:30

Isaiah Farahbakhsh, Chrystopher L. Nehaniv

http://arxiv.org/abs/2007.01896v2, http://arxiv.org/pdf/2007.01896v2

math.DS

th

We investigate how to model the beliefs of an agent who becomes more aware. We use the framework of Halpern and Rego (2013) by adding probability, and define a notion of a model transition that describes constraints on how, if an agent becomes aware of a new formula $\phi$ in state $s$ of a model $M$, she transitions to state $s^*$ in a model $M^*$. We then discuss how such a model can be applied to information disclosure.

Dynamic Awareness

2020-07-06 18:28:22

Joseph Y. Halpern, Evan Piermont

http://arxiv.org/abs/2007.02823v1, http://arxiv.org/pdf/2007.02823v1

cs.AI

th

This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov, in the extended context allowing for possibly different discount rates for both parties. The agent's problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirement. A Golden Parachute is a situation where the agent ceases any effort at some positive stopping time, and receives a payment afterwards, possibly under the form of a lump sum payment, or of a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov, where the only requirement is a positive agent's marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent's utility function has a too negative curvature at zero. In the general case, we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov's solution). We show that different discount factors induce a face-lifted utility function, which allows to reduce the analysis to a setting similar to the equal discount rates one. Finally, we also confirm that an agent with small reservation utility may have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility than his participation value.

Is there a Golden Parachute in Sannikov's principal-agent problem?

2020-07-10 15:50:49

Dylan Possamaï, Nizar Touzi

http://arxiv.org/abs/2007.05529v2, http://arxiv.org/pdf/2007.05529v2

econ.TH

th

Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These inequalities are simple to apply and can be used to generalize and extend previous results or to derive new results. We apply our inequalities to quantify the notion "more risk averse" provided in \cite{pratt1978risk}. We also apply our results in other applications from different fields, including risk measures, Poisson approximation, moment generating functions, log-likelihood functions, and Hermite-Hadamard type inequalities.

New Jensen-type inequalities and their applications

2020-07-18 01:08:02

Bar Light

http://arxiv.org/abs/2007.09258v3, http://arxiv.org/pdf/2007.09258v3

math.OC

th

Most online platforms strive to learn from interactions with users, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We study the interplay between exploration and competition: how such platforms balance the exploration for learning and the competition for users. Here users play three distinct roles: they are customers that generate revenue, they are sources of data for learning, and they are self-interested agents which choose among the competing platforms. We consider a stylized duopoly model in which two firms face the same multi-armed bandit problem. Users arrive one by one and choose between the two firms, so that each firm makes progress on its bandit problem only if it is chosen. Through a mix of theoretical results and numerical simulations, we study whether and to what extent competition incentivizes the adoption of better bandit algorithms, and whether it leads to welfare increases for users. We find that stark competition induces firms to commit to a "greedy" bandit algorithm that leads to low welfare. However, weakening competition by providing firms with some "free" users incentivizes better exploration strategies and increases welfare. We investigate two channels for weakening the competition: relaxing the rationality of users and giving one firm a first-mover advantage. Our findings are closely related to the "competition vs. innovation" relationship, and elucidate the first-mover advantage in the digital economy.

Competing Bandits: The Perils of Exploration Under Competition

2020-07-20 17:19:08

Guy Aridor, Yishay Mansour, Aleksandrs Slivkins, Zhiwei Steven Wu

http://arxiv.org/abs/2007.10144v7, http://arxiv.org/pdf/2007.10144v7

cs.GT

th

This paper studies continuous-time optimal contracting in a hierarchy problem which generalises the model of Sung (2015). The hierarchy is modeled by a series of interlinked principal-agent problems, leading to a sequence of Stackelberg equilibria. More precisely, the principal can contract with the managers to incentivise them to act in her best interest, despite only observing the net benefits of the total hierarchy. Managers in turn subcontract with the agents below them. Both agents and managers independently control in continuous time a stochastic process representing their outcome. First, we show through a continuous-time adaptation of Sung's model that, even if the agents only control the drift of their outcome, their manager controls the volatility of their continuation utility. This first simple example justifies the use of recent results on optimal contracting for drift and volatility control, and therefore the theory of second-order backward stochastic differential equations, developed in the theoretical part of this paper, dedicated to a more general model. The comprehensive approach we outline highlights the benefits of considering a continuous-time model and opens the way to obtain comparative statics. We also explain how the model can be extended to a large-scale principal-agent hierarchy. Since the principal's problem can be reduced to only an $m$-dimensional state space and a $2m$-dimensional control set, where $m$ is the number of managers immediately below her, and is therefore independent of the size of the hierarchy below these managers, the dimension of the problem does not explode.

Continuous-time incentives in hierarchies

2020-07-21 15:47:29

Emma Hubert

http://arxiv.org/abs/2007.10758v1, http://arxiv.org/pdf/2007.10758v1

math.OC

th

In multi-agent environments in which coordination is desirable, the history of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies with a significant environmental footprint or high social cost persist despite the successful development of more environmentally friendly and/or socially efficient alternatives. The displacement of the status quo is hindered by entrenched economic interests and network effects. To exacerbate matters, the standard mechanism design approaches based on centralized authorities with the capacity to use preferential subsidies to effectively dictate system outcomes are not always applicable to modern decentralized economies. What other types of mechanisms are feasible? In this paper, we develop and analyze a mechanism that induces transitions from inefficient lock-ins to superior alternatives. This mechanism does not exogenously favor one option over another -- instead, the phase transition emerges endogenously via a standard evolutionary learning model, Q-learning, where agents trade-off exploration and exploitation. Exerting the same transient influence to both the efficient and inefficient technologies encourages exploration and results in irreversible phase transitions and permanent stabilization of the efficient one. On a technical level, our work is based on bifurcation and catastrophe theory, a branch of mathematics that deals with changes in the number and stability properties of equilibria. Critically, our analysis is shown to be structurally robust to significant and even adversarially chosen perturbations to the parameters of both our game and our behavioral model.

Catastrophe by Design in Population Games: Destabilizing Wasteful Locked-in Technologies

2020-07-25 10:55:15

Stefanos Leonardos, Iosif Sakos, Costas Courcoubetis, Georgios Piliouras

http://arxiv.org/abs/2007.12877v1, http://arxiv.org/pdf/2007.12877v1

cs.GT

th

We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model. Using the response strategy framework, we describe how the actions of the players can bring the network into a steady configuration, starting from an out-of-equilibrium one. We obtain these configurations using game-theoretical tools, and describe the results using Ising parameters. We exhaust the two-player case, giving a detailed account of all the equilibrium possibilities. Going to three players, we generalize the Ising model and compare the equilibrium solutions of three representative types of network. We find that players that are not directly linked retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. Finally, we conclude that certain parameters of the equilibrium states are network independent, which opens up the possibility of an analytical description of asymmetric games played on networks.

Asymmetric games on networks: towards an Ising-model representation

2020-11-05 13:23:38

A. D. Correia, L. L. Leestmaker, H. T. C. Stoof

http://arxiv.org/abs/2011.02739v3, http://arxiv.org/pdf/2011.02739v3

physics.soc-ph

th

We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for consistency are established. Finally, we propose a numerical method based on the derived models and present numerical results.

Multiscale Control of Stackelberg Games

2020-11-06 18:05:43

Michael Herty, Sonja Steffensen, Anna Thünen

http://arxiv.org/abs/2011.03405v1, http://arxiv.org/pdf/2011.03405v1

math.OC

th

Understanding the likelihood for an election to be tied is a classical topic in many disciplines including social choice, game theory, political science, and public choice. Despite a large body of literature and the common belief that ties are rare, little is known about how rare ties are in large elections except for a few simple positional scoring rules under the i.i.d. uniform distribution over the votes, known as the Impartial Culture (IC) in social choice. In particular, little progress was made after Marchant explicitly posed the likelihood of k-way ties under IC as an open question in 2001. We give an asymptotic answer to the open question for a wide range of commonly studied voting rules under a model that is much more general and realistic than i.i.d. models (especially IC) -- the smoothed social choice framework by Xia that was inspired by the celebrated smoothed complexity analysis by Spielman and Teng. We prove dichotomy theorems on the smoothed likelihood of ties under positional scoring rules, edge-order-based rules, and some multi-round score-based elimination rules, which include commonly studied voting rules such as plurality, Borda, veto, maximin, Copeland, ranked pairs, Schulze, STV, and Coombs as special cases. We also complement the theoretical results by experiments on synthetic data and real-world rank data on Preflib. Our main technical tool is an improved dichotomous characterization on the smoothed likelihood for a Poisson multinomial variable to be in a polyhedron, which is proved by exploring the interplay between the V-representation and the matrix representation of polyhedra and might be of independent interest.

How Likely Are Large Elections Tied?

2020-11-07 18:16:04

Lirong Xia

http://arxiv.org/abs/2011.03791v3, http://arxiv.org/pdf/2011.03791v3

cs.GT

th

This paper is an axiomatic study of consistent approval-based multi-winner rules, i.e., voting rules that select a fixed-size group of candidates based on approval ballots. We introduce the class of counting rules and provide an axiomatic characterization of this class based on the consistency axiom. Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin--Courant rule. Our results demonstrate the variety of multi-winner rules and illustrate three different, orthogonal principles that multi-winner voting rules may represent: individual excellence, diversity, and proportionality.

Consistent Approval-Based Multi-Winner Rules

2017-04-08 10:29:43

Martin Lackner, Piotr Skowron

http://arxiv.org/abs/1704.02453v6, http://arxiv.org/pdf/1704.02453v6

cs.GT

th

I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my analysis to perfect stable matchings, where every agent on both sides is matched.

Saturating stable matchings

2020-11-11 22:59:50

Muhammad Maaz

http://dx.doi.org/10.1016/j.orl.2021.06.013, http://arxiv.org/abs/2011.06046v2, http://arxiv.org/pdf/2011.06046v2

cs.GT

th

We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to her, and at the same time, raise capital for her firm's enterprise from other agents she is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collateral contracts in handling the strategic risk that can propagate to a systemic risk throughout the network in a cascade of defaults. We take a mechanism-design approach and solve for the optimal scheme of collateral contracts that capital raisers offer their investors. These contracts aim at sustaining the efficient level of investment as a unique Nash equilibrium, while minimizing the total collateral. Our main results contrast the network environment with its non-network counterpart (where the sets of investors and capital raisers are disjoint). We show that for acyclic investment networks, the network environment does not necessitate any additional collaterals, and systemic risk can be fully handled by optimal bilateral collateral contracts between capital raisers and their investors. This is, unfortunately, not the case for cyclic investment networks. We show that bilateral contracting will not suffice to resolve systemic risk, and the market will need an external entity to design a global collateral scheme for all capital raisers. Furthermore, the minimum total collateral that will sustain the efficient level of investment as a unique equilibrium may be arbitrarily higher, even in simple cyclic investment networks, compared with its corresponding non-network environment. Additionally, we prove computational-complexity results, both for a single enterprise and for networks.

Optimal Collaterals in Multi-Enterprise Investment Networks

2020-11-12 10:59:46

Moshe Babaioff, Yoav Kolumbus, Eyal Winter

http://dx.doi.org/10.1145/3485447.3512053, http://arxiv.org/abs/2011.06247v3, http://arxiv.org/pdf/2011.06247v3

cs.GT

th

We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. Our setup generalizes the well-known Kyle model, by dropping the assumption of a terminal time at which fundamental information is revealed so to describe a stationary market, while retaining agents' rationality and asymmetric information. We investigate the stationary equilibrium for arbitrary Gaussian noise trades and fundamental information, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay. Our model provides a testable relation between volatility of prices, magnitude of fluctuations in fundamentals and level of volume traded in the market.

A Stationary Kyle Setup: Microfounding propagator models

2020-11-20 10:23:35

Michele Vodret, Iacopo Mastromatteo, Bence Tóth, Michael Benzaquen

http://dx.doi.org/10.1088/1742-5468/abe702, http://arxiv.org/abs/2011.10242v3, http://arxiv.org/pdf/2011.10242v3

q-fin.TR

th

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors.

Monotone additive statistics

2021-02-01 06:43:06

Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz

http://arxiv.org/abs/2102.00618v4, http://arxiv.org/pdf/2102.00618v4

econ.TH

th

I study the measurement of scientists' influence using bibliographic data. The main result is an axiomatic characterization of the family of citation-counting indices, a broad class of influence measures which includes the renowned h-index. The result highlights several limitations of these indices: they are not suitable to compare scientists across different fields, and they cannot account for indirect influence. I explore how these limitations can be overcome by using richer bibliographic information.

The Limits of Citation Counts

2017-11-07 22:22:02

Antonin Macé

http://arxiv.org/abs/1711.02695v3, http://arxiv.org/pdf/1711.02695v3

cs.DL

th

We study network games in which players choose both the partners with whom they associate and an action level (e.g., effort) that creates spillovers for those partners. We introduce a framework and two solution concepts, extending standard approaches for analyzing each choice in isolation: Nash equilibrium in actions and pairwise stability in links. Our main results show that, under suitable order conditions on incentives, stable networks take simple forms. The first condition concerns whether links create positive or negative payoff spillovers. The second concerns whether actions are strategic complements to links, or strategic substitutes. Together, these conditions yield a taxonomy of the relationship between network structure and economic primitives organized around two network architectures: ordered overlapping cliques and nested split graphs. We apply our model to understand the consequences of competition for status, to microfound matching models that assume clique formation, and to interpret empirical findings that highlight unintended consequences of group design.

Games on Endogenous Networks

2021-02-02 19:27:00

Evan Sadler, Benjamin Golub

http://arxiv.org/abs/2102.01587v7, http://arxiv.org/pdf/2102.01587v7

econ.TH

th

We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

Cutoff stability under distributional constraints with an application to summer internship matching

2021-02-05 03:11:46

Haris Aziz, Anton Baychkov, Peter Biro

http://arxiv.org/abs/2102.02931v2, http://arxiv.org/pdf/2102.02931v2

cs.GT

th

We study a game theoretic model of standardized testing for college admissions. Students are of two types; High and Low. There is a college that would like to admit the High type students. Students take a potentially costly standardized exam which provides a noisy signal of their type. The students come from two populations, which are identical in talent (i.e. the type distribution is the same), but differ in their access to resources: the higher resourced population can at their option take the exam multiple times, whereas the lower resourced population can only take the exam once. We study two models of score reporting, which capture existing policies used by colleges. The first policy (sometimes known as "super-scoring") allows students to report the max of the scores they achieve. The other policy requires that all scores be reported. We find in our model that requiring that all scores be reported results in superior outcomes in equilibrium, both from the perspective of the college (the admissions rule is more accurate), and from the perspective of equity across populations: a student's probability of admission is independent of their population, conditional on their type. In particular, the false positive rates and false negative rates are identical in this setting, across the highly and poorly resourced student populations. This is the case despite the fact that the more highly resourced students can -- at their option -- either report a more accurate signal of their type, or pool with the lower resourced population under this policy.

Best vs. All: Equity and Accuracy of Standardized Test Score Reporting

2021-02-15 22:27:22

Sampath Kannan, Mingzi Niu, Aaron Roth, Rakesh Vohra

http://arxiv.org/abs/2102.07809v1, http://arxiv.org/pdf/2102.07809v1

cs.GT

th

In this paper, we investigate two heterogeneous triopoly games where the demand function of the market is isoelastic. The local stability and the bifurcation of these games are systematically analyzed using the symbolic approach proposed by the author. The novelty of the present work is twofold. On one hand, the results of this paper are analytical, which are different from the existing results in the literature based on observations through numerical simulations. In particular, we rigorously prove the existence of double routes to chaos through the period-doubling bifurcation and through the Neimark-Sacker bifurcation. On the other hand, for the special case of the involved firms having identical marginal costs, we acquire the necessary and sufficient conditions of the local stability for both models. By further analyzing these conditions, it seems that that the presence of the local monopolistic approximation (LMA) mechanism might have a stabilizing effect for heterogeneous triopoly games with the isoelastic demand.

Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand

2021-12-11 14:01:20

Xiaoliang Li

http://arxiv.org/abs/2112.05950v1, http://arxiv.org/pdf/2112.05950v1

math.DS

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. Despite the simplicity of this problem, a classical result by Myerson and Satterthwaite (1983) affirms the impossibility of designing a mechanism which is simultaneously efficient, incentive compatible, individually rational, and budget balanced. This impossibility result fostered an intense investigation of meaningful trade-offs between these desired properties. Much work has focused on approximately efficient fixed-price mechanisms, i.e., Blumrosen and Dobzinski (2014; 2016), Colini-Baldeschi et al. (2016), which have been shown to fully characterize strong budget balanced and ex-post individually rational direct revelation mechanisms. All these results, however, either assume some knowledge on the priors of the seller/buyer valuations, or a black box access to some samples of the distributions, as in D{\"u}tting et al. (2021). In this paper, we cast for the first time the bilateral trade problem in a regret minimization framework over rounds of seller/buyer interactions, with no prior knowledge on the private seller/buyer valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different models of feedback and private valuations, using as benchmark the best fixed price in hindsight. More precisely, we prove the following bounds on the regret: $\bullet$ $\widetilde{\Theta}(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms); $\bullet$ $\widetilde{\Theta}(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities; $\bullet$ $\Theta(T)$ for realistic feedback and seller/buyer valuations with bounded densities; $\bullet$ $\Theta(T)$ for realistic feedback and independent seller/buyer valuations; $\bullet$ $\Theta(T)$ for the adversarial setting.

A Regret Analysis of Bilateral Trade

2021-02-16 11:53:17

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

http://dx.doi.org/10.1145/3465456.3467645, http://arxiv.org/abs/2102.08754v1, http://arxiv.org/pdf/2102.08754v1

cs.LG

th

Critical decisions like loan approvals, medical interventions, and college admissions are guided by predictions made in the presence of uncertainty. In this paper, we prove that uncertainty has a disparate impact. While it imparts errors across all demographic groups, the types of errors vary systematically: Groups with higher average outcomes are typically assigned higher false positive rates, while those with lower average outcomes are assigned higher false negative rates. We show that additional data acquisition can eliminate the disparity and broaden access to opportunity. The strategy, which we call Affirmative Information, could stand as an alternative to Affirmative Action.

The Disparate Impact of Uncertainty: Affirmative Action vs. Affirmative Information

2021-02-19 19:40:47

Claire Lazar Reich

http://arxiv.org/abs/2102.10019v4, http://arxiv.org/pdf/2102.10019v4

stat.ML

th

We study a repeated persuasion setting between a sender and a receiver, where at each time $t$, the sender observes a payoff-relevant state drawn independently and identically from an unknown prior distribution, and shares state information with the receiver, who then myopically chooses an action. As in the standard setting, the sender seeks to persuade the receiver into choosing actions that are aligned with the sender's preference by selectively sharing information about the state. However, in contrast to the standard models, the sender does not know the prior, and has to persuade while gradually learning the prior on the fly. We study the sender's learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the prior distribution. Our main positive result is an algorithm that, with high probability, is persuasive across all rounds and achieves $O(\sqrt{T\log T})$ regret, where $T$ is the horizon length. The core philosophy behind the design of our algorithm is to leverage robustness against the sender's ignorance of the prior. Intuitively, at each time our algorithm maintains a set of candidate priors, and chooses a persuasion scheme that is simultaneously persuasive for all of them. To demonstrate the effectiveness of our algorithm, we further prove that no algorithm can achieve regret better than $\Omega(\sqrt{T})$, even if the persuasiveness requirements were significantly relaxed. Therefore, our algorithm achieves optimal regret for the sender's learning problem up to terms logarithmic in $T$.

Learning to Persuade on the Fly: Robustness Against Ignorance

2021-02-20 00:02:15

You Zu, Krishnamurthy Iyer, Haifeng Xu

http://arxiv.org/abs/2102.10156v1, http://arxiv.org/pdf/2102.10156v1

cs.GT

th

We introduce a new algorithm for finding stable matchings in multi-sided matching markets. Our setting is motivated by a PhD market of students, advisors, and co-advisors, and can be generalized to supply chain networks viewed as $n$-sided markets. In the three-sided PhD market, students primarily care about advisors and then about co-advisors (consistent preferences), while advisors and co-advisors have preferences over students only (hence they are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and student-co-advisor pairs may not be mutually acceptable (e.g., a student may not want to work with an advisor or co-advisor and vice versa). We show that three-sided stable matchings always exist, and present an algorithm that, in time quadratic in the market size (up to log factors), finds a three-sided stable matching using any two-sided stable matching algorithm as matching engine. We illustrate the challenges that arise when not all advisor-co-advisor pairs are compatible. We then generalize our algorithm to $n$-sided markets with quotas and show how they can model supply chain networks. Finally, we show how our algorithm outperforms the baseline given by [Danilov, 2003] in terms of both producing a stable matching and a larger number of matches on a synthetic dataset.

Finding Stable Matchings in PhD Markets with Consistent Preferences and Cooperative Partners

2021-02-23 21:10:46

Maximilian Mordig, Riccardo Della Vecchia, Nicolò Cesa-Bianchi, Bernhard Schölkopf

http://arxiv.org/abs/2102.11834v2, http://arxiv.org/pdf/2102.11834v2

cs.GT

th

Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time series of an index variable composed of stocks in this market is observed.

A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon

2021-12-12 21:15:33

Stefan Bornholdt

http://arxiv.org/abs/2112.06290v1, http://arxiv.org/pdf/2112.06290v1

physics.soc-ph

th

Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.

Discord and Harmony in Networks

2021-02-26 08:56:01

Andrea Galeotti, Benjamin Golub, Sanjeev Goyal, Rithvik Rao

http://arxiv.org/abs/2102.13309v1, http://arxiv.org/pdf/2102.13309v1

econ.TH