pwc-archive/papers-with-abstracts huggingface dataset:
The importance of being discrete: on the inaccuracy of continuous approximations in auction theory
Authors: Itzhak Rasooly, Carlos Gavidia-Calderon
Date: 2020-06-04 00:00:00

While auction theory views bids and valuations as continuous variables, real-world auctions are necessarily discrete. In this paper, we use a combination of analytical and computational methods to investigate whether incorporating discreteness substantially changes the predictions of auction theory, focusing on the case of uniformly distributed valuations so that our results bear on the majority of auction experiments. In some cases, we find that introducing discreteness changes little. For example, the first-price auction with two bidders and an even number of values has a symmetric equilibrium that closely resembles its continuous counterpart and converges to its continuous counterpart as the discretisation goes to zero. In others, however, we uncover discontinuity results. For instance, introducing an arbitrarily small amount of discreteness into the all-pay auction makes its symmetric, pure-strategy equilibrium disappear; and appears (based on computational experiments) to rob the game of pure-strategy equilibria altogether. These results raise questions about the continuity approximations on which auction theory is based and prompt a re-evaluation of the experimental literature.
Efficient allocations in double auction markets
Authors: Teemu Pennanen
Date: 2020-01-05 00:00:00
Tasks: Descriptive

This paper proposes a simple descriptive model of discrete-time double auction markets for divisible assets. As in the classical models of exchange economies, we consider a finite set of agents described by their initial endowments and preferences. Instead of the classical Walrasian-type market models, however, we assume that all trades take place in a centralized double auction where the agents communicate through sealed limit orders for buying and selling. We find that, under nonstrategic bidding, the double auction clears with zero trades precisely when the agents' current holdings are on the Pareto frontier. More interestingly, the double auctions implement Adam Smith's "invisible hand" in the sense that, when starting from disequilibrium, repeated double auctions lead to a sequence of allocations that converges to individually rational Pareto allocations.
Evolutionarily Stable (Mis)specifications: Theory and Applications
Authors: Kevin He, Jonathan Libgober
Date: 2020-12-30 00:00:00

Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their environment through repeated play. The relative stability of (mis)specifications depends on their adherents' equilibrium payoffs. A key mechanism is the learning channel: the endogeneity of perceived best replies due to inference. We characterize when a rational society is only vulnerable to invasion by some misspecification through the learning channel. The learning channel leads to new stability phenomena, and can confer an evolutionary advantage to otherwise detrimental biases in economically relevant applications.
Local Dominance
Authors: Emiliano Catonini, Jingyi Xue
Date: 2020-12-28 00:00:00

We define notions of dominance between two actions in a dynamic game. Local dominance considers players who have a blurred view of the future and compare the two actions by first focusing on the outcomes that may realize at the current stage. When considering the possibility that the game may continue, they can only check that the local comparison is not overturned under the assumption of "continuing in the same way" after the two actions (in a newly defined sense). Despite the lack of forward planning, local dominance solves dynamic mechanisms that were found easy to play and implements social choice functions that cannot be implemented in obviously-dominant strategies.
Calculated Boldness: Optimizing Financial Decisions with Illiquid Assets
Authors: Stanislav Shalunov, Alexei Kitaev, Yakov Shalunov, Arseniy Akopyan
Date: 2020-12-26 00:00:00

We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the expected logarithm of total capital including both capital in play and the external capital. For games with multiple rounds, we determine the optimal strategy through dynamic programming and construct a close approximation through the WKB method. The strategy can be described in terms of short-term utility functions, with risk aversion depending on the ratio of the amount in the game to the external money. Thus, a rational player's behavior varies between conservative play that approaches Kelly strategy as they are able to invest a larger fraction of total wealth and extremely aggressive play that maximizes linear expectation when a larger portion of their capital is locked away. Because you always have expected future productivity to account for as external resources, this goes counter to the conventional wisdom that super-Kelly betting is a ruinous proposition.
Negative votes to depolarize politics
Authors: Karthik H. Shankar
Date: 2020-12-26 00:00:00

The controversies around the 2020 US presidential elections certainly casts serious concerns on the efficiency of the current voting system in representing the people's will. Is the naive Plurality voting suitable in an extremely polarized political environment? Alternate voting schemes are gradually gaining public support, wherein the voters rank their choices instead of just voting for their first preference. However they do not capture certain crucial aspects of voter preferences like disapprovals and negativities against candidates. I argue that these unexpressed negativities are the predominant source of polarization in politics. I propose a voting scheme with an explicit expression of these negative preferences, so that we can simultaneously decipher the popularity as well as the polarity of each candidate. The winner is picked by an optimal tradeoff between the most popular and the least polarizing candidate. By penalizing the candidates for their polarization, we can discourage the divisive campaign rhetorics and pave way for potential third party candidates.
A Theory of Updating Ambiguous Information
Authors: Rui Tang
Date: 2020-12-26 00:00:00
Tasks: Sensitivity

We introduce a new updating rule, the conditional maximum likelihood rule (CML) for updating ambiguous information. The CML formula replaces the likelihood term in Bayes' rule with the maximal likelihood of the given signal conditional on the state. We show that CML satisfies a new axiom, increased sensitivity after updating, while other updating rules do not. With CML, a decision maker's posterior is unaffected by the order in which independent signals arrive. CML also accommodates recent experimental findings on updating signals of unknown accuracy and has simple predictions on learning with such signals. We show that an information designer can almost achieve her maximal payoff with a suitable ambiguous information structure whenever the agent updates according to CML.
Feasible Joint Posterior Beliefs
Authors: Itai Arieli, Yakov Babichenko, Fedor Sandomirskiy, Omer Tamuz
Date: 2020-02-26 00:00:00

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.
The Probabilistic Serial and Random Priority Mechanisms with Minimum Quotas
Authors: Marek Bojko
Date: 2020-12-20 00:00:00

Consider the problem of assigning indivisible objects to agents with strict ordinal preferences over objects, where each agent is interested in consuming at most one object, and objects have integer minimum and maximum quotas. We define an assignment to be feasible if it satisfies all quotas and assume such an assignment always exists. The Probabilistic Serial (PS) and Random Priority (RP) mechanisms are generalised based on the same intuitive idea: Allow agents to consume their most preferred available object until the total mass of agents yet to be allocated is exactly equal to the remaining amount of unfilled lower quotas; in this case, we restrict agents' menus to objects which are yet to fill their minimum quotas. We show the mechanisms satisfy the same criteria as their classical counterparts: PS is ordinally efficient, envy-free and weakly strategy-proof; RP is strategy-proof, weakly envy-free but not ordinally efficient.
The role of time estimation in decreased impatience in Intertemporal Choice
Authors: Camila S. Agostino Peter M. E. Claessens, Fuat Balci, Yossi Zana
Date: 2020-12-19 00:00:00

The role of specific cognitive processes in deviations from constant discounting in intertemporal choice is not well understood. We evaluated decreased impatience in intertemporal choice tasks independent of discounting rate and non-linearity in long-scale time representation; nonlinear time representation was expected to explain inconsistencies in discounting rate. Participants performed temporal magnitude estimation and intertemporal choice tasks. Psychophysical functions for time intervals were estimated by fitting linear and power functions, while discounting functions were estimated by fitting exponential and hyperbolic functions. The temporal magnitude estimates of 65% of the participants were better fit with power functions (mostly compression). 63% of the participants had intertemporal choice patterns corresponding best to hyperbolic functions. Even when the perceptual bias in the temporal magnitude estimations was compensated in the discounting rate computation, the data of 8 out of 14 participants continued exhibiting temporal inconsistency. The results suggest that temporal inconsistency in discounting rate can be explained to different degrees by the bias in temporal representations. Non-linearity in temporal representation and discounting rate should be evaluated on an individual basis. Keywords: Intertemporal choice, temporal magnitude, model comparison, impatience, time inconsistency
Decision Making under Uncertainty: A Game of Two Selves
Authors: Jianming Xia
Date: 2020-12-14 00:00:00
Tasks: Decision Making, Decision Making Under Uncertainty, Vocal Bursts Valence Prediction

In this paper we characterize the niveloidal preferences that satisfy the Weak Order, Monotonicity, Archimedean, and Weak C-Independence Axioms from the point of view of an intra-personal, leader-follower game. We also show that the leader's strategy space can serve as an ambiguity aversion index.
Misspecified Beliefs about Time Lags
Authors: Yingkai Li, Harry Pei
Date: 2020-12-14 00:00:00

We examine the long-term behavior of a Bayesian agent who has a misspecified belief about the time lag between actions and feedback, and learns about the payoff consequences of his actions over time. Misspecified beliefs about time lags result in attribution errors, which have no long-term effect when the agent's action converges, but can lead to arbitrarily large long-term inefficiencies when his action cycles. Our proof uses concentration inequalities to bound the frequency of action switches, which are useful to study learning problems with history dependence. We apply our methods to study a policy choice game between a policy-maker who has a correctly specified belief about the time lag and the public who has a misspecified belief.
The Cost of Information: The Case of Constant Marginal Costs
Authors: Luciano Pomatto, Philipp Strack, Omer Tamuz
Date: 2018-12-11 00:00:00

We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with Blackwell monotonicity and a continuity condition, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states.
Applications of Mean Field Games in Financial Engineering and Economic Theory
Authors: Rene Carmona
Date: 2020-12-09 00:00:00

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract theory.
Occupational segregation in a Roy model with composition preferences
Authors: Haoning Chen, Miaomiao Dong, Marc Henry, Ivan Sidorov
Date: 2020-12-08 00:00:00
Tasks: Diversity

We propose a model of labor market sector self-selection that combines comparative advantage, as in the Roy model, and sector composition preference. Two groups choose between two sectors based on heterogeneous potential incomes and group compositions in each sector. Potential incomes incorporate group specific human capital accumulation and wage discrimination. Composition preferences are interpreted as reflecting group specific amenity preferences as well as homophily and aversion to minority status. We show that occupational segregation is amplified by the composition preferences and we highlight a resulting tension between redistribution and diversity. The model also exhibits tipping from extreme compositions to more balanced ones. Tipping occurs when a small nudge, associated with affirmative action, pushes the system to a very different equilibrium, and when the set of equilibria changes abruptly when a parameter governing the relative importance of pecuniary and composition preferences crosses a threshold.
Competition, Politics, & Social Media
Authors: Benson Tsz Kin Leung, Pinar Yildirim
Date: 2020-12-06 00:00:00

An increasing number of politicians are relying on cheaper, easier to access technologies such as online social media platforms to communicate with their constituency. These platforms present a cheap and low-barrier channel of communication to politicians, potentially intensifying political competition by allowing many to enter political races. In this study, we demonstrate that lowering costs of communication, which allows many entrants to come into a competitive market, can strengthen an incumbent's position when the newcomers compete by providing more information to the voters. We show an asymmetric bad-news-good-news effect where early negative news hurts the challengers more than the positive news benefit them, such that in aggregate, an incumbent politician's chances of winning is higher with more entrants in the market. Our findings indicate that communication through social media and other platforms can intensify competition, how-ever incumbency advantage may be strengthened rather than weakened as an outcome of higher number of entrants into a political market.
Pick-an-object Mechanisms
Authors: Inácio Bó, Rustamdjan Hakimov
Date: 2020-12-02 00:00:00
Tasks: Object

We introduce a new family of mechanisms for one-sided matching markets, denoted pick-an-object (PAO) mechanisms. When implementing an allocation rule via PAO, agents are asked to pick an object from individualized menus. These choices may be rejected later on, and these agents are presented with new menus. When the procedure ends, agents are assigned the last object they picked. We characterize the allocation rules that can be sequentialized by PAO mechanisms, as well as the ones that can be implemented in a robust truthful equilibrium. We justify the use of PAO as opposed to direct mechanisms by showing that its equilibrium behavior is closely related to the one in obviously strategy-proof (OSP) mechanisms, but implements commonly used rules, such as Gale-Shapley DA and top trading cycles, which are not OSP-implementable. We run laboratory experiments comparing truthful behavior when using PAO, OSP, and direct mechanisms to implement different rules. These indicate that agents are more likely to behave in line with the theoretical prediction under PAO and OSP implementations than their direct counterparts.
Assignment Maximization
Authors: Mustafa Oğuz Afacan, Inácio Bó, Bertan Turhan
Date: 2020-12-02 00:00:00
Tasks: Fairness

We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -- in terms of number of assignments -- in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium.
Strategy-proof Popular Mechanisms
Authors: Mustafa Oğuz Afacan, Inácio Bó
Date: 2020-12-02 00:00:00

We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time slots in public tennis courts. Given an allocation, groups of agents who would prefer an alternative allocation might challenge it. An assignment is popular if it is not challenged by another one. By assuming that agents' ability to challenge allocations can be represented by weighted votes, we characterize the conditions under which popular allocations might exist and when these can be implemented via strategy-proof mechanisms. Serial dictatorships that use orderings consistent with the agents' weights are not only strategy-proof and Pareto efficient, but also popular, whenever these assignments exist. We also provide a new characterization for serial dictatorships as the only mechanisms that are popular, strategy-proof, non-wasteful, and satisfy a consistency condition.
On Absolute and Relative Change
Authors: Silvan Brauen, Philipp Erpf, Micha Wasem
Date: 2020-11-30 00:00:00
Tasks: Relation

Based on an axiomatic approach we propose two related novel one-parameter families of indicators of change which put in a relation classical indicators of change such as absolute change, relative change and the log-ratio.
Temporal assortment of cooperators in the spatial prisoner's dilemma
Authors: Tim Johnson, Oleg Smirnov
Date: 2020-11-29 00:00:00

We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its choice of when to implement that strategy across a set of discrete time slots. Cooperators evolve to fixation regularly in the model when we add time slots to lattices and small-world networks, and their portion of the population grows, albeit slowly, when organisms interact in a scale-free network. This selection for cooperators occurs across a wide variety of time slots and it does so even when a crucial condition for the evolution of cooperation on graphs is violated--namely, when the ratio of benefits to costs in the PD does not exceed the number of spatially-adjacent organisms.
Compactification of Extensive Game Structures and Backward Dominance Procedure
Authors: Shuige Liu
Date: 2019-05-01 00:00:00

We study the relationship between invariant transformations on extensive game structures and backward dominance procedure (BD), a generalization of the classical backward induction introduced in Perea (2014). We show that behavioral equivalence with unambiguous orderings of information sets, a critical property that guarantees BD's applicability, can be characterized by the classical Coalescing and a modified Interchange/Simultanizing in Battigalli et al. (2020). We also give conditions on transformations that improve BD's efficiency. In addition, we discuss the relationship between transformations and Bonanno (2014)'s generalized backward induction.
Short Term Electricity Market Designs: Identified Challenges and Promising Solutions
Authors: Lina Silva-Rodriguez, Anibal Sanjab, Elena Fumagalli, Ana Virag, Madeleine Gibescu
Date: 2020-11-09 00:00:00

The electricity market, which was initially designed for dispatchable power plants and inflexible demand, is being increasingly challenged by new trends, such as the high penetration of intermittent renewables and the transformation of the consumers energy space. To accommodate these new trends and improve the performance of the market, several modifications to current market designs have been proposed in the literature. Given the vast variety of these proposals, this paper provides a comprehensive investigation of the modifications proposed in the literature as well as a detailed assessment of their suitability for improving market performance under the continuously evolving electricity landscape. To this end, first, a set of criteria for an ideal market design is proposed, and the barriers present in current market designs hindering the fulfillment of these criteria are identified. Then, the different market solutions proposed in the literature, which could potentially mitigate these barriers, are extensively explored. Finally, a taxonomy of the proposed solutions is presented, highlighting the barriers addressed by each proposal and the associated implementation challenges. The outcomes of this analysis show that even though each barrier is addressed by at least one proposed solution, no single proposal is able to address all the barriers simultaneously. In this regard, a future-proof market design must combine different elements of proposed solutions to comprehensively mitigate market barriers and overcome the identified implementation challenges. Thus, by thoroughly reviewing this rich body of literature, this paper introduces key contributions enabling the advancement of the state-of-the-art towards increasingly efficient electricity market.