nep-gth New Economics Papers
on Game Theory
Issue of 2015‒10‒04
23 papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. An Experiment on Lowest Unique Integer Games By Takashi Yamada; Nobuyuki Hanaki
  2. Repeated Games with General Discounting By Ichiro Obara; Jaeok Park
  3. A Fine Rule From a Brutish World? An Experiment on Endogenous Punishment Institution and Trust By H. Sun; M. Bigoni
  4. The Impact of Redistribution Mechanisms in the Vote with the Wallet Game: Experimental Results By Leonardo Becchetti; Vittorio Pelligra; Francesco Salustri
  5. Frictions in Internet Auctions with Many Traders: a Counterexample By Donna, Javier; Schenone, Pablo; Veramendi, Gregory
  6. Efficiency and Stability in Large Matching Markets By Yeon-Koo Che; Olivier Tercieux
  7. Undiscounted Bandit Games By Keller, Godfrey; Rady, Sven
  8. Cournot tatonnement in aggregative games with monotone best responses By Kukushkin, Nikolai S.
  9. Conformist Preferences in Mixed-Motive Games By Naef, Michael; Sontuoso, Alessandro
  10. Competitive Equilibrium and Singleton Cores in Generalized Matching Problems By Jaeok Park
  11. First Price Auctions with General Information Structures: Implications for Bidding and Revenue By Dirk Bergemann; Benjamin Brooks; Stephen Morris
  12. High-frequency limit of Nash equilibria in a market impact game with transient price impact By Alexander Schied; Elias Strehle; Tao Zhang
  13. Information and Market Power By Dirk Bergemann; Tibor Heumann; Stephen Morris
  14. Doing it now, later, or never By Cingiz K.; Flesch J.; Herings P.J.J.; Predtetchinski A.
  15. Repeated Implementation By Azacis, Helmuts; Vida, Péter
  16. Foreclosure Auctions By Niedermayer, Andreas; Shneyerov, Artyom; Xu, Pia
  17. Robust Mechanisms: the curvature case By Vinicius Carrasco; Vitor Farinha Luz; Paulo Monteiro; Humberto Moreira
  18. Payoff Equivalence of Efficient Mechanisms in Large Matching Markets By Yeon-Koo Che; Olivier Tercieux
  19. An Experimental Study of Uncertainty in Coordination Games By Ioannou, Christos A.; Makris, Miltiadis
  20. Vertical Collective Action: Addressing Vertical Asymmetries in Watershed Management By Cárdenas, Juan-Camilo; Rodriguez, Luz Angela; Johnson, Nancy
  21. An Analysis of Top Trading Cycles in Two-Sided Matching Markets By Yeon-Koo Che; Olivier Tercieux
  22. Fair Allocation of Disputed Properties By Biung-Ghi Ju; Juan D. Moreno-Ternero
  23. Networks, Frictions, and Price Dispersion By Donna, Javier; Schenone, Pablo; Veramendi, Gregory

  1. By: Takashi Yamada (Faculty of Global and Science Studies, Yamaguchi University, Japan); Nobuyuki Hanaki (Université Nice Sophia Antipolis; GREDEG-CNRS; IUF)
    Abstract: We experimentally study Lowest Unique Integer Games (LUIGs). In a LUIG, N (>3) players submit a positive integer up to M and the player choosing the smallest number not chosen by anyone else wins. LUIGs are simplified versions of real systems such as lottery games and Lowest/Highest Unique Bid Auctions that have been attracting attention from scholars, yet experimental studies are still scarce. Here, we consider four LUIGs with N = {3; 4} and M = {3; 4}. We find that (a) choices made by a majority of subjects over 50 rounds of a LUIG were not significantly different from that in the symmetric mixed-strategy Nash equilibrium (MSE) of the LUIG; however, (b) those subjects who behaved significantly differently from what the MSE predicts won the game more frequently than those who behaved similarly to what the MSE predicts.
    Keywords: Lowest Unique Integer Game, Laboratory Experiment
    JEL: C72 C92
    Date: 2015–09
  2. By: Ichiro Obara (University of California); Jaeok Park (Yonsei University)
    Abstract: We introduce a general class of time discounting, which includes time-inconsistent ones, into repeated games with perfect monitoring. A strategy prole is called an agent subgame perfect equilibrium if there is no protable one-shot deviation at any history. We characterize strongly symmetric agent subgame perfect equilibria for repeated games with symmetric stage game. We nd that the harshest punishment takes different forms given different biases. When players are future biased, the harshest punishment is supported by a version of stick-and-carrot strategy. When players are present biased, the harshest punishment may take a more complex form. In particular, the worst punishment path may need to be cyclical. We also nd that the worst punishment payoff is different from the stage game minmax payoff even when players are patient. For some class of discounting, we show that the worst punishment payoff is larger than the stage game minmax payoff with present bias and smaller than the stage game minmax payo with future bias. We also characterize the set of limit equilibrium payoffs as the length of periods converges to 0, without changing the intertemporal structure of biases.
    Keywords: Hyperbolic Discounting, Present Bias, Repeated Game, Time Inconsistency
    JEL: C73 D03
    Date: 2015–10
  3. By: H. Sun; M. Bigoni
    Abstract: By means of a laboratory experiment, we study the impact of the endogenous adoption of a collective punishment mechanism within a one-shot binary trust game. The experiment comprises three games. In the first one, the only equilibrium strategy is not to trust, and not to reciprocate. In the second we exogenously introduce a sanctioning rule that imposes on untrustworthy second-movers a penalty proportional to the number of those who reciprocate trust. This generates a second equilibrium where everybody trusts and reciprocates. In the third game, the collective punishment mechanism is adopted through majority-voting. In line with the theory, we find that the exogenous introduction of the punishment mechanism significantly increases trustworthiness, and to a lesser extent also trust. However, in the third game the majority of subjects vote against it: subjects seem to be unable to endogenously adopt an institution which, when exogenously imposed, proves to be efficiency enhancing.
    JEL: C72 C92 D72
    Date: 2015–09
  4. By: Leonardo Becchetti (University of Rome Tor Vergata); Vittorio Pelligra (University of Cagliari, CRENoS); Francesco Salustri (DEDI, University of Rome "Tor Vergata")
    Abstract: We use the Vote-with-the-Wallet game (VWG) to model socially or environmentally responsible consumption, an increasingly relevant but still under-researched phenomenon. Based on a theoretical model outlining game equilibria and the parametric interval of the related multiplayer prisoners’ dilemma (PD) we evaluate with a controlled lab experiment players’ behavior in the game and test the effects of an ex post redistribution mechanism between defectors and cooperators. Our findings document that the redistribution mechanism interrupts cooperation decay and stabilizes the share of cooperators at a level significantly higher, even though inferior to the Nash equilibrium.
    Keywords: vote with the wallet, prisoner’s dilemma, lab experiment
    JEL: C72 C73 C91 M14
    Date: 2015–10–02
  5. By: Donna, Javier; Schenone, Pablo; Veramendi, Gregory
    Abstract: Peters and Severinov (2006) (PS henceforth) characterize a perfect Bayesian equilibrium (PBE) in a competing auctions environment, where all buyers are linked to all the sellers. PS characterize a PBE using a simple bidding rule, whereby buyers select in which auction to bid. In this note we show that when buyers are linked with a subset of the sellers (i.e. when there are search frictions), the PS bidding rule is no longer guaranteed to be efficient nor a PBE of the competing auctions game of PS. Our results indicate that researchers should be cautious when using the PS bidding rule to make inference about the behavior of buyers and sellers in a market where frictions are present such as eBay.
    Keywords: Auctions; Internet; Frictions; Networks
    JEL: C73 C78 D44 L00
    Date: 2015–09–01
  6. By: Yeon-Koo Che (Dept. of Economics, Columbia University); Olivier Tercieux (Dept. of Economics, Paris School of Economics)
    Abstract: We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals’ preferences and priorities are drawn randomly. When agents’ preferences are uncorrelated, then both efficiency and stability can be achieved in an asymptotic sense via standard mechanisms such as deferred acceptance and top trading cycles. When agents’ preferences are correlated over objects, however, these mechanisms are either inefficient or unstable even in an asymptotic sense. We propose a variant of deferred acceptance that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible. This new mechanism performs well in a counterfactual calibration based on New York City school choice data.
    Keywords: Large matching markets, Pareto efficiency, Stability, Fairness, Payoff equivalence, Asymptotic efficiency, and Asymptotic stability
    JEL: C70 D61 D63
    Date: 2015–07
  7. By: Keller, Godfrey; Rady, Sven
    Abstract: We analyze continuous-time games of strategic experimentation with two-armedbandits when there is no discounting. We show that for all specifications of priorbeliefs and payoff-generating processes that satisfy some separability condition, the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the expected current payoff of the risky arm and the expected full-information payoff, given current information. The separability condition holds in a variety of models that have been explored in the literature, all of which assume that the risky arm’s expected payoff per unit of time is time-invariant and actual payoffs are generated by a process with independent and stationary increments. The separability condition does not hold when the expected payoff per unit of time is subject to state-switching.
    Keywords: Strategic Experimentation; Two-Armed Bandit; Markov-Perfect Equilibrium
    JEL: C73 D83
    Date: 2015–09–21
  8. By: Kukushkin, Nikolai S.
    Abstract: This paper establishes the acyclicity of Cournot tatonnement in a strategic game with aggregation and monotone best responses, under the broadest assumptions on aggregation rules allowing the Huang-Dubey-Haimanko-Zapechelnyuk-Jensen trick to work and with minimal topological restrictions.
    Keywords: Cournot tatonnement; Cournot potential; aggregative game; monotone best responses
    JEL: C72
    Date: 2015–09–24
  9. By: Naef, Michael; Sontuoso, Alessandro
    Abstract: We examine a novel class of conformist preferences which falls within the realm of belief-dependent motivations in that the peers’ expectations about others’ behavior may affect every group-member’s welfare. Similar other-regarding motivations, like guilt-aversion, have been inferred from evidence of a belief-behavior correlation but the issue of causality has been disputed. In examining conformism we propose a design that verifies the presence of the relevant causality direction while ruling out alternative other-regarding motivations. Our data reveal “self-servingly conformist” behavior in that subjects choose to match their strategy to the peers’ expectations when it is in their interest to do so.
    Keywords: conformist preferences, consensus effects, belief-dependent utility, guilt aversion, social norms, trust
    JEL: C72 C91
    Date: 2015–09–13
  10. By: Jaeok Park (Yonsei University)
    Abstract: We study competitive equilibria in generalized matching problems. We show that, if there is a competitive matching, then it is unique and the core is a singleton consisting of the competitive matching. That is, a singleton core is necessary for the existence of competitive equilibria. We also show that a competitive matching exists if and only if the matching produced by the top trading cycles algorithm is feasible, in which case it is the unique competitive matching. Hence, we can use the top trading cycles algorithm to test whether a competitive equilibrium exists and to construct a competitive equilibrium if one exists. Lastly, in the context of bilateral matching problems, we compare the condition for the existence of competitive matchings with existing suffcient conditions for the existence or uniqueness of stable matchings and show that it is weaker than the existing conditions.
    Keywords: matching, competitive equilibrium, core, top trading cycles algorithm
    JEL: C78 D51
    Date: 2015–10
  11. By: Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University)
    Abstract: This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others' values. Revenue is minimized when buyers are uncertain about whether they will win or lose and incentive constraints are binding for all upward bid deviations. We provide further analytic results on possible welfare outcomes and report computational methods which work when we do not have analytic solutions. Many of our results generalize to asymmetric value distributions. We apply these results to study how entry fees and reserve prices impact the welfare bounds.
    Keywords: First price auction, Information structure, Bayes correlated equilibrium, Private values, Interdependent values, Common values, Revenue, surplus, Welfare bounds, Reserve price, Entry fee
    JEL: C72 D44 D82 D83
    Date: 2015–08
  12. By: Alexander Schied; Elias Strehle; Tao Zhang
    Abstract: We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic transaction costs of size $\theta\ge0$. We show that, for $\theta=0$, equilibrium strategies and costs will oscillate indefinitely between two accumulation points. For $\theta>0$, however, both strategies and costs will converge towards limits that are independent of $\theta$. We then show that the limiting strategies form a Nash equilibrium for a continuous-time version of the model with $\theta$ equal to a certain critical value $\theta^*>0$, and that the corresponding expected costs coincide with the high-frequency limits of the discrete-time equilibrium costs. For $\theta\neq\theta^*$, however, continuous-time Nash equilibria will typically not exist. Our results permit us to give mathematically rigorous proofs of numerical observations made in Schied and Zhang [arXiv:1305.4013, 2013]. In particular, we provide a range of model parameters for which the limiting expected costs of both agents are decreasing functions of $\theta$. That is, for sufficiently high trading speed, raising additional transaction costs can reduce the expected costs of all agents.
    Date: 2015–09
  13. By: Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Dept. of Economics, Yale University); Stephen Morris (Dept. of Economics, Princeton University)
    Abstract: We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We establish our results by providing a characterization of the set of all joint distributions over demands and payoff states that can arise in equilibrium under any information structure. In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot competition. We find that the first and second moments of the equilibrium distribution respond very differently to the private information of the agents under these two market structures. The first moment of the equilibrium demand, the average demand, is more sensitive to the nature of the private information in demand function competition, reflecting the strategic impact of private information. By contrast, the second moments are less sensitive to the private information, reflecting the common conditioning on the price among the agents.
    Keywords: Demand function competition, Supply function competition, Price impact, Market power, Incomplete information, Bayes correlated equilibrium, Volatility, Moments restrictions, Linear best responses, Quadratic payoffs
    JEL: C72 C73 D43 D83 G12
    Date: 2015–08
  14. By: Cingiz K.; Flesch J.; Herings P.J.J.; Predtetchinski A. (GSBE)
    Abstract: We study centipede games played by an infinite sequence of players. Following the literature on time-inconsistent preferences, we distinguish two types of decision makers, naive and sophisticated, and the corresponding solution concepts, nave -equilibrium and sophisticated -equilibrium. We show the existence of both naive and sophisticated -equilibria for each positive . Under the assumption that the payoff functions are upper semicontinuous, we furthermore show that there exist both naive and sophisticated 0-equilibria in pure strategies. We also compare the probability to stop of a naive versus a sophisticated decision maker and show that a sophisticated decision maker stops earlier.
    Keywords: Game Theory and Bargaining Theory: General; Consumer Economics: Theory; Welfare Economics: General; Conflict; Conflict Resolution; Alliances; Intertemporal Consumer Choice; Life Cycle Models and Saving;
    JEL: C70 D11 D60 D74 D91
    Date: 2015
  15. By: Azacis, Helmuts; Vida, Péter
    Abstract: We prove that a social choice function is repeatedly implementable if and only if it is dynamically monotonic when the number of agents is at least three. We show how to test dynamic monotonicity by building an associated repeated game. It follows that a weaker version of Maskin monotonicity is necessary and sufficient among the social choice functions that are efficient. As an application, we show that utilitarian social choice functions, which can only be one-shot implemented with side-payments, are repeatedly implementable, as continuation payoffs can play the role of transfers. Under some additional assumptions, our results also apply when the number of agents is two.
    Keywords: Mechanism Design; Dynamic Monotonicity; Efficiency; Repeated Implementation; Repeated Games; Approximation of the Equilibrium Set; Sufficient and Necessary Condition
    JEL: C73 D71
    Date: 2015–09–17
  16. By: Niedermayer, Andreas; Shneyerov, Artyom; Xu, Pia
    Abstract: We develop a novel theory of real estate foreclosure auctions, which have the special feature that the lender acts as a seller for low and as a buyer for high prices. The theory yields several empirically testable predictions concerning the strategic behavior of the agents, both under symmetric and asymmetric information. Using novel data from Palm Beach County (FL, US), we �nd evidence of both strategic behavior and asymmetric information, with the lender being the informed party. Moreover, the data are consistent with moral hazard in mortgage securitization: banks collect less information about the value of the mortgage collateral.
    Keywords: Foreclosure Auctions; Asymmetric Information; Bunching; Discontinuous Strategies; Securitization
    JEL: C72 D44 D82 G21
    Date: 2015–09–22
  17. By: Vinicius Carrasco (Department of Economics PUC-Rio); Vitor Farinha Luz (European University Institute and the Department of Economics, The University of British Columbia); Paulo Monteiro (FGV/EPGE); Humberto Moreira (FGV/EPGE)
    Abstract: This note considers the problem of a principal (she) who faces a privately informed agent (he) and only knows one moment of the distribution from which his types are drawn. Payoffs are non-linear in the allocation and the principal maximizes her worst-case expected profits. We recast the robust design problem as a zero-sum game played by the principal and an adversarial nature who seeks to minimize her expected payoffs. The robust mechanism and the worst case distribution are, then, the Nash equilibrium of such game. A robustness property of the optimal mechanism imposes restrictions on the principal’s ex-post profit function. These restrictions then lead to the optimal mechanism. The robust mechanism entails exclusion of low types and distortions at the intensive margin that (in a precise sense) are larger than what those that prevail in standard Bayesian mechanism design problems.
    Date: 2015–06
  18. By: Yeon-Koo Che (Dept. of Economics, Columbia University); Olivier Tercieux (Dept. of Economics, Paris School of Economics)
    Abstract: We study Pareto efficient mechanisms in matching markets when the number of agents is large and individual preferences are randomly drawn from a class of distributions, allowing for both common and idiosyncratic shocks. We show that, as the market grows large, all Pareto efficient mechanisms -- including top trading cycles, serial dictatorship, and their randomized variants -- are uniformly asymptotically payoff equivalent “up to the renaming of agents,” yielding the utilitarian upper bound in the limit. This result implies that, when the conditions of our model are met, policy makers need not discriminate among Pareto efficient mechanisms based on the aggregate payoff distribution of participants.
    Keywords: Large matching markets, Pareto efficiency, Payoff equivalence
    JEL: C70 D61 D63
    Date: 2015–07
  19. By: Ioannou, Christos A.; Makris, Miltiadis
    Abstract: Global games and Poisson games have been proposed to address equilibrium indeterminacy in Coordination games. The former assume that agents face idiosyncratic uncertainty about economic fundamentals to capture disperse information, whereas the latter model the number of actual players as a Poisson random variable to capture population uncertainty in large games. Given that their predictions differ, it is imperative to understand which type of uncertainty drives empirical behavior in macroeconomic environments with strategic complementarities. Recent experimental literature finds mixed results on whether subjects' behavior is similar in Global and Common Knowledge Coordination games, and hence on whether idiosyncratic uncertainty about economic fundamentals is an important determinant of subjects' behavior. Poisson Coordination games have not been investigated experimentally. We fill this gap. Our findings suggest that uncertainty about the number of actual players may influence subjects' behavior. Crucially, such behavior is consistent with the theoretical prediction of Poisson Coordination games.
    Date: 2015–09–23
  20. By: Cárdenas, Juan-Camilo; Rodriguez, Luz Angela; Johnson, Nancy
    Abstract: Watersheds and irrigation systems have the characteristic of connecting people vertically by water flows. The location of users along these systems defines their role in the provision and appropriation of water which adds complexity to the potential for cooperation. Verticality thus imposes a challenge to collective action. This paper presents the results of field experiments conducted in four watersheds of Colombia (South America) and Kenya (East Africa) to study the role that location plays in affecting trust and cooperation in decisions regarding to provision and appropriation of water. We recruited 639 watersheds inhabitants from upstream, midstream and downstream locations in these basins and conducted two field experiments: the Irrigation Game and the Water Trust Game. The Irrigation Game (Cardenas et al, 2013; Janssen et al, 2011) involves decisions regarding to the provision and appropriation of water where the location in the system is randomly assigned. The Water Trust Game is an adaptation of the trust game (Berg et al 1995) framed around water and economic compensation flows where we explicitly reveal the actual upstream or downstream location of the two players. The results of the two games show that location affect water provision and distribution and that reciprocity and trust are key motivations for upstream-downstream cooperation. Yet, both experiments also suggest that the lack of trust from downstream players towards upstream players may restrict the possibilities of cooperation among watershed users.
    Keywords: Collective Action, Verticality, Watersheds, Field Experiments, Irrigation Game, Trust Game, Water Trust Game, Payments for Environmental Services, Colombia, Kenya., Environmental Economics and Policy, Productivity Analysis, Q0, Q2, C9,
    Date: 2015–01
  21. By: Yeon-Koo Che (Dept. of Economics, Columbia University); Olivier Tercieux (Dept. of Economics, Paris School of Economics)
    Abstract: We study top trading cycles in a two-sided matching environment (Abdulkadiroglu and Sonmez (2003)) under the assumption that individuals’ preferences and objects’ priorities are drawn iid uniformly. The distributions of agents’ preferences and objects’ priorities remaining after a given round of TTC depend nontrivially on the exact history of the algorithm up to that round (and so need not be uniform iid). Despite the nontrivial history-dependence of evolving economies, we show that the number of individuals/objects assigned at each round follows a simple Markov chain and we explicitly derive the transition probabilities.
    Keywords: Random matching markets, Markov property
    JEL: C70 D61 D63
    Date: 2015–07
  22. By: Biung-Ghi Ju (Department of Economics, Seoul National University); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain)
    Abstract: We model problems of allocating disputed properties as generalized exchange economies in which agents have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient to satisfy all individual claims. In this context, we investigate three categories of fairness in the initial assignment of rights, in the transaction of rights, and in the end-state allocation, their implications and relations. To do so, we explore allocation rules represented by a composition of a rights-assignment rule (to assign each profile of claims individual property rights over the endowment) and Walrasian or other individually rational exchange. Using variants of fairness based on no-envy as end-state principles, we provide axiomatic characterizations of the three focal egalitarian rights-assignment rules, known in the literature on rationing problems as constrained equal awards, constrained equal losses, and proportional rules. We apply our results to problems of greenhouse gas emissions and contested water rights.
    Keywords: fairness, claims, no-envy, individual rationality, egalitarianism, efficiency, Walrasian exchange
    JEL: D63 D71
    Date: 2015–09
  23. By: Donna, Javier; Schenone, Pablo; Veramendi, Gregory
    Abstract: This paper models frictions in buyer-seller markets using networks, where buyers are linked with a subset of sellers and sellers are linked with a subset of buyers. Sparser networks are associated with higher search frictions. We use the model to characterize pairwise stable allocations and their supporting prices. Our approach allows for network effects, where a buyer who is not linked to a seller affects the price obtained by that seller. Network effects generate the central finding of our paper: even relatively sparse networks lead to price distributions and allocations that are close to the perfectly competitive outcome where the law of one price holds. We then investigate the role of network effects in a dynamic setting by studying wages in the context of an on-the-job search model. We find two novel predictions relative to the search literature. Lowering frictions (so that workers receive job offers at a higher rate) leads to: (1) lower worker mobility and lower expected wage growth and (2) lower expected wages in markets with high unemployment. We argue that our framework is suited to the analysis of a wide range of real-world markets, such as the labor market and buyer-seller trading platforms like eBay or Amazon.
    Keywords: Networks; Matching; Auctions; Competition; Frictions; Price Dispersion
    JEL: C78 D44 J31 L00
    Date: 2015–07–17

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