nep-gth New Economics Papers
on Game Theory
Issue of 2021‒03‒15
24 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit By Arjun Krishnan U M; Colin Benjamin
  2. Selective memory of a psychological agent By Hagenbach, Jeanne; Koessler, Frédéric
  3. Paying to Match: Decentralized Markets with Information Frictions By Agranov Agranov; Ahrash Dianat; Larry Samuelson; Leeat Yariv
  4. Individual versus Group Choices of Repeated Game Strategies: A Strategy Method Approach By Timothy N. Cason; Vai-Lam Mui
  5. Allocation Rules for Multi-choice Games with a Permission Tree Structure By David Lowing
  6. Third-Party Punishment: Retribution or Deterrence? By Fangfang Tan; Erte Xiao
  7. Acquisition, (Mis)use and Dissemination of Information: The Blessing of Cursedness and Transparency By Franz Ostrizek; Elia Sartori
  8. Mapping an Information Design Game into an All-Pay Auction By Oleg Muratov
  9. Repeated Games with Switching Costs -- Stationary vs History Independent Strategies By Yevgeny Tsodikovich; Xavier Venel; Anna Zseleva
  10. Screening while Controlling an Externality By Franz Ostrizek; Elia Sartori
  11. Artificial Intelligence and Pricing: The Impact of Algorithm Design By John Asker; Chaim Fershtman; Ariel Pakes
  12. Imperfect Tacit Collusion and Asymmetric Price Transmission By Bulutay, Muhammed; Hales, David; Julius, Patrick; Tasch, Weiwei
  13. A Dynkin game on assets with incomplete information on the return By Tiziano de Angelis; Fabien Gensbittel; Stéphane Villeneuve
  14. Obfuscation and rational inattention in digitalized markets By Janssen, Aljoscha; Kasinger, Johannes
  15. Pollution, partial privatization and the effect of ambient charges By Ohnishi, Kazuhiro
  16. Collusion in Quality-Segmented Markets By Bos, Iwan; Marini, Marco A.
  17. Informational Robustness of Common Belief in Rationality By Gabriel Ziegler
  18. Are Efficient Bargaining Power Disparities Unfair? An Experimental Test By Aaron Nicholas; Birendra Rai
  19. Optional Disclosure and Observational Learning By Diefeng Peng; Yulei Rao; Xianming Sun; Erte Xiao
  20. Minimum cost spanning tree problems as value sharing problems By Christian Trudeau
  21. The Evolution of Sectarianism By Ille, Sebastian
  22. A veil of ignorance: uncertain and ambiguous individual productivity supports stable contributions to a public good By Zack Dorner; Steven Tucker; Gazi Hassan
  23. Intellectual Property Infringement by Foreign Firms: Import Protection through the ITC or Court By James A. Brander; Barbara J. Spencer
  24. Limited-Tenure Concessions for Collective Goods By Nicolas Quérou; Agnes Tomini; Christopher Costello

  1. By: Arjun Krishnan U M; Colin Benjamin
    Abstract: How cooperation evolves and manifests itself in the thermodynamic or infinite player limit of social dilemma games is a matter of intense speculation. Various analytical methods have been proposed to analyse the thermodynamic limit of social dilemmas. In a previous work [Chaos Solitons and fractals 135, 109762(2020)] involving one among us, two of those methods, Hamiltonian Dynamics(HD) and Nash equilibrium(NE) mapping were compared. The inconsistency and incorrectness of HD approach vis-a-vis NE mapping was brought to light. In this work we compare a third analytical method, i.e, Darwinian evolution(DE) with NE mapping and a numerical agent based approach. For completeness, we give results for HD approach as well. In contrast to HD which involves maximisation of payoffs of all individuals, in DE, payoff of a single player is maximised with respect to its nearest neighbour. While, HD utterly fails as compared to NE mapping, DE method gives a false positive for game magnetisation -- the net difference between the fraction of cooperators and defectors -- when payoffs obey the condition a+d=b+c, wherein a, d represent the diagonal elements and b, c the off diagonal elements in symmetric social dilemma games. When either a+d =/= b+c or, when one looks at average payoff per player, DE method fails much like the HD approach. NE mapping and numerical agent based method on the other hand agree really well for both game magnetisation as well as average payoff per player for the social dilemmas in question, i.e., Hawk-Dove game and Public goods game. This paper thus bring to light the inconsistency of the DE method vis-a-vis both NE mapping as well as a numerical agent based approach.
    Date: 2021–02
  2. By: Hagenbach, Jeanne; Koessler, Frédéric
    Abstract: We consider a single psychological agent whose utility depends on his action, the state of the world, and the belief that he holds about that state. The agent is initially informed about the state and decides whether to memorize it, otherwise he has no recall. We model the memorization process by a multi-self game in which the privately informed first self voluntarily discloses information to the second self, who has identical preferences and acts upon the disclosed information. We identify broad categories of psychological utility functions for which there exists an equilibrium in which every state is voluntarily memorized. In contrast, if there are exogenous failures in the memorization process, then the agent memorizes states selectively. In this case, we characterize the partially informative equilibria for common classes of psychological utilities. If the material cost of forgetting is low, then the agent only memorizes good enough news. Otherwise, only extreme news are voluntarily memorized.
    Keywords: Multi-self game,disclosure games,imperfect recall,selective memory,motivated beliefs,psychological games,anticipatory utility
    JEL: C72 D82
    Date: 2021
  3. By: Agranov Agranov (California Institute of Technology); Ahrash Dianat (University of Essex); Larry Samuelson (Yale University); Leeat Yariv (Princeton University)
    Abstract: We experimentally study decentralized one-to-one matching markets with transfers. We vary the information available to participants, complete or incomplete, and the surplus structure, supermodular or submodular. Several insights emerge. First, while markets often culminate in efficient matchings, stability is more elusive, reflecting the difficulty of arranging attendant transfers. Second, incomplete information and submodularity present hurdles to efficiency and especially stability; their combination drastically diminishes stability's likelihood. Third, matchings form "from the top down" in complete-information supermodular markets, but exhibit many more and less-obviously ordered offers otherwise. Last, participants' market positions matter far more than their dynamic bargaining styles for outcomes.
    JEL: C78 D82 D83
    Date: 2021–01
  4. By: Timothy N. Cason; Vai-Lam Mui
    Abstract: We study experimentally the indefinitely repeated noisy prisoner’s dilemma, in which random events can change an intended action to its opposite. We investigate whether groups choose Always Defect less and use lenient or forgiving strategies more than individuals, and how decision-makers experiment with different strategies by letting them choose from an extensive list of repeated game strategies. We find that groups use forgiving and tit-for-tat strategies more than individuals. Always Defect, however, is the most popular strategy for both groups and individuals. Groups and individuals cooperate at similar rates overall, and they seldom experiment with different strategies in later supergames.
    Keywords: Laboratory Experiment; Cooperation; Repeated Games; Strategy
    JEL: C73 C92
    Date: 2019–06
  5. By: David Lowing (Univ Lyon, UJM Saint-Etienne, GATE Lyon Saint-Etienne UMR 5824, F-42023 Saint-Etienne, France)
    Abstract: We consider multi-choice cooperative games with a permission tree structure. Multi-choice games are a generalization of a cooperative transferable utility games in which each player has several activity levels. In addition, a permission tree structure models a situation in which a player needs permission from another player to cooperate. In this framework, the influence of a permission structure on the possibility of cooperation may have several interpretations depending on the context. In this paper, we investigate several of these interpretations and introduce for each of them a new allocation rule that we axiomatically characterize.
    Keywords: Multi-choice games, Multi-choice Permission value, Permission (tree) structures
    JEL: C71
    Date: 2021
  6. By: Fangfang Tan; Erte Xiao
    Abstract: We conduct an experiment to examine the role of retribution and deterrence in motivating third party punishment. In particular, we consider how the role of these two motives may differ according to whether a third party is a group or an individual. In a one-shot prisoner’s dilemma game with third party punishment, we find groups punish more when the penalty embeds deterrence than when it can only be retributive. In contrast, individual third parties’ punishment decisions do not vary on whether the punishment has any deterrent effect. In general, third party groups are less likely to impose punishment than individuals even though the punishment is costless for third parties.
    Keywords: Third-party punishment, group decision making, retribution, deterrence, social dilemmas, experiment
    JEL: C72 C92 D63 D70
    Date: 2019–06
  7. By: Franz Ostrizek (briq - Institute on Behavior & Inequality); Elia Sartori (CSEF)
    Abstract: This paper studies strategic interactions where players observe statistics of others’ actions, focusing on: First, the endogeneity of the precision of such aggregate information as signals of the fundamental; and second, agents’ well-documented difficulty in making inference based on such signals. We conduct our analysis in a beauty contest game with information acquisition, adapting cursed equilibrium to model agents limited ability to process aggregative information. To discipline information acquisition choices in this setting with incorrect information use, we define a novel notion of cursed expectations equilibrium with information acquisition: Agents assess the value of private information according to a subjective envelope condition, as they correctly anticipate their actions and (incorrectly) deem them optimal. We show that there is inefficiently low acquisition and use of private information in the rational benchmark due to an information dissemination externality. Despite suboptimal use, ursed agents rely more heavily on their private information which pushes information acquisition towards its efficient level and causes an initial increase in welfare. Transparency crowds out private information but always increases the endogenous precision of the aggregative signal and welfare, while other policy instruments can have paradoxical effects due to their interaction with cursedness. Finally, we explore the behavior and welfare of an atomistic rational agent playing against a cursed crowd and demonstrate that transparency may be an elitist policy.
    Keywords: Information Acquisition, Transparency, Cursed Equilibrium, Information Dissemination, Aggregative Information.
    JEL: C72 D62 D83 D90
    Date: 2021–02–03
  8. By: Oleg Muratov
    Abstract: I show that there exists a mapping between a class of information design games with multiple senders and a class of all-pay auctions. I fully characterize this mapping and show how to use it to find equilibria in the information design game. Such an approach could be applied to establish mappings between other classes of information design games, on the one hand, and contests, on the other.
    Date: 2021–03
  9. By: Yevgeny Tsodikovich; Xavier Venel; Anna Zseleva
    Abstract: We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, which depend solely on the previous action of the player (and not the entire history), and we provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the player is limited to playing completely history-independent strategies and provide a full characterization of the value and optimal strategies in this case. Naturally, this limitation worsens his situation. We deduce a bound on his loss in the general case as well as more precise bounds when more assumptions regarding the game or the switching costs are introduced.
    Date: 2021–02
  10. By: Franz Ostrizek (briq - Institute on Behavior & Inequality); Elia Sartori (CSEF)
    Abstract: We propose a tractable framework to introduce externalities into a monopolist screening model. Agents differ both in their payoff type and their influence, i.e. how strongly their action affects the aggregate externality. Applications range from non-linear pricing of a network good, to taxation or subsidization of industries that produce externalities (e.g. pollution and human capital formation). When both dimensions are unobserved (full screening) the optimal allocation satisfies lexicographic monotonicity: within a payoff-type, the monopolist optimally tilts the allocation towards influential agents to increase the externality, while standard IC drives monotonicity across payoff-types. We characterize the solution through a two-step ironing procedure that addresses the nonmonotonicity in virtual values arising from the countervailing impact of payoff-types and influence. The allocation is inefficient if and only if the payoff-type is unobservable. Only influence is observable, equilibrium utility can vary across the latter as it is used as a signal of the payoff-type. We provide sufficient conditions for (expected) rents from influence to emerge.
    Date: 2021–02–03
  11. By: John Asker; Chaim Fershtman; Ariel Pakes
    Abstract: The behavior of artificial intelligences algorithms (AIAs) is shaped by how they learn about their environment. We compare the prices generated by AIAs that use different learning protocols when there is market interaction. Asynchronous learning occurs when the AIA only learns about the return from the action it took. Synchronous learning occurs when the AIA conducts counterfactuals to learn about the returns it would have earned had it taken an alternative action. The two lead to markedly different market prices. When future profits are not given positive weight by the AIA, synchronous updating leads to competitive pricing, while asynchronous can lead to pricing close to monopoly levels. We investigate how this result varies when either counterfactuals can only be calculated imperfectly and/or when the AIA places a weight on future profits.
    JEL: C72 C73 D43 D82 K21 L1 L13 L4 L51 O33
    Date: 2021–03
  12. By: Bulutay, Muhammed; Hales, David; Julius, Patrick; Tasch, Weiwei
    Abstract: We investigate the role tacit collusion plays in Asymmetric Price Transmission (APT), the tendency of prices to respond more rapidly to positive than to negative cost shocks. Using a laboratory experiment that isolates the effects of tacit collusion, we observe APT pricing behavior in markets with 3, 4, 6, and 10 sellers, but not in duopolies. Furthermore, we find that sellers accurately forecast others’ prices, but nevertheless consistently set their own prices above the profit-maximizing response, particularly in the periods immediately following negative shocks. Overall, our findings support theories in which tacit collusion plays a central role in APT.
    Keywords: Asymmetric Price Transmission,Tacit Collusion,Oligopolistic Competition,Market Power,Rockets and Feathers
    JEL: D43 L13 C92 C72 C73
    Date: 2021
  13. By: Tiziano de Angelis; Fabien Gensbittel (TSM - Toulouse School of Management Research - UT1 - Université Toulouse 1 Capitole - CNRS - Centre National de la Recherche Scientifique - TSM - Toulouse School of Management - UT1 - Université Toulouse 1 Capitole); Stéphane Villeneuve (TSM - Toulouse School of Management Research - UT1 - Université Toulouse 1 Capitole - CNRS - Centre National de la Recherche Scientifique - TSM - Toulouse School of Management - UT1 - Université Toulouse 1 Capitole)
    Abstract: This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion (X; Y ). Then we characterize the existence of a Nash equilibrium in pure strategies in which each player stops at the hitting time of (X; Y ) to a set with moving boundary. A detailed description of the stopping sets for the two players is provided along with global C1 regularity of the value function.
    Date: 2020
  14. By: Janssen, Aljoscha; Kasinger, Johannes
    Abstract: This paper studies the behavior of competing firms in a duopoly with rational inattentive consumers. Firms play a sequential game in which they decide to obfuscate their individual prices before competing on price. Probabilistic demand functions are endogenously determined by the consumers' optimal information strategy, which depends on the firms' obfuscation choice and the consumers' unrestricted prior beliefs. We show that the game may result in an obfuscation equilibrium with high prices where both firms obfuscate and a transparency equilibrium with low prices and no obfuscation, providing an argument for market regulation. Lower information costs and asymmetric prior beliefs about prices reduce the probability of an obfuscation equilibrium. Using data on Sweden, we document a decrease in price complexity and corresponding prices in the market for mobile phone subscriptions in the last two decades. Our model rationalizes these changes and explains why complexity and high prices persist in some but not all digitalized markets.
    Keywords: Rational Inattention,Obfuscation,Price Competition,Digitalized Markets
    JEL: D11 D21 D43
    Date: 2021
  15. By: Ohnishi, Kazuhiro
    Abstract: This paper considers a mixed Cournot duopoly model comprising a private firm and a partially privatized public firm to reassess the effect of an increase in ambient charges, and compares the result of this study with that obtained from private Cournot duopoly competition. The paper demonstrates that our result is about the same as that of private Cournot duopoly competition.
    Keywords: ambient charge; Cournot duopoly; environmental regulation; partial privatization; pollution
    JEL: C72 D21 L33 Q58
    Date: 2021–02–27
  16. By: Bos, Iwan; Marini, Marco A.
    Abstract: This paper analyzes price collusion in a repeated game with two submarkets; a standard and a premium quality segment. Within this setting, we study four types of price-fixing agreement: (i) a segment-wide cartel in the premium submarket only, (ii) a segment-wide cartel in the standard submarket only, (iii) two segment-wide cartels, and (iv) an industry-wide cartel. We present a complete characterization of the collusive pricing equilibrium and examine the corresponding effeect on market shares and welfare. Partial cartels operating in a sufficiently large segment lose market share and the industry-wide cartel prefers to maintain market shares at pre-collusive levels. The impact on consumer and social welfare critically depends on the cost of producing quality. Moreover, given that there is a cartel, more collusion can be beneficial for society as a whole.
    Keywords: Partial Cartels, Price Collusion, Market Segmentation, Vertical Differentiation.
    JEL: D21 D23 D24 D4 D43 D6
    Date: 2020–10–01
  17. By: Gabriel Ziegler
    Abstract: I explore the implications of informational robustness under the assumptions of common belief in rationality. That is, predictions for incomplete-information games which are valid across all possible information structures. First, I address this question from a global perspective and then generalize the analysis to allow for localized informational robustness.
    Date: 2021–03
  18. By: Aaron Nicholas; Birendra Rai
    Abstract: A key question in labor and contract law is when does bargaining power disparity become too large to be considered `impermissible'? It has largely been debated from the potentially conflicting perspectives of efficiency and fairness. These debates exhibit the intuitively plausible but empirically untested presumption that efficient bargaining power disparities can be unfair. The paper focuses on ex-post bargaining between agents locked in a relationship without a complete contract wherein surplus may ultimately be realized with or without mutual consent. We propose a consent-based definition to categorize a bargaining power disparity as either efficient or inefficient by treating surplus realized without mutual consent as an imperfect substitute for surplus realized with mutual consent. In order to categorize a power disparity as either fair or unfair, we draw upon some legal doctrines to propose a two-sided definition that accounts for the perspectives of both the weaker and the stronger bargaining parties. The experiment provides no robust evidence to support the presumption that economically efficient power disparities can be unfair.
    Keywords: Bargaining power, consent, efficiency, fairness, law, contract, experiment
    JEL: K0 C72 C91 D63
    Date: 2019–06
  19. By: Diefeng Peng; Yulei Rao; Xianming Sun; Erte Xiao
    Abstract: Observational learning theories often assume that people’s actions can be observed. However, in many naturally-occurring environments, individuals can choose whether to disclose their behavior to others. We provide theoretical analysis of observational learning under optional disclosure conditions. We further examine empirically how individuals decide whether to reveal decisions. Although we find evidence for other-regarding disclosure behavior, our findings highlight the importance of providing public information about how the disclosure behavior affects others.
    Keywords: Observational learning; Information cascade; Optional disclosure; Other-regarding preferences
    JEL: C91 D82 D83 D64 D91
    Date: 2019–06
  20. By: Christian Trudeau (Department of Economics, University of Windsor)
    Abstract: Minimum cost spanning tree (mcst) problems study situations in which agents must connect to a source to obtain a good, with the cost of building an edge being independent of the number of users. We reinterpret mcst problems as value sharing problems, and show that the folk and cycle-complete solutions, two of the most studied cost-sharing solutions for mcst problems, do not share values in a consistent way. More precisely, two mcst problems yielding the same value sharing problem might lead to value being shared in different ways. However, they satisfy a weaker version of the property that applies only to elementary problems, in which the cost on an edge can only be 0 or 1. The folk solution satisfies the version related to the public approach, while the cycle-complete solution satisfies the one related to the private approach, which differ depending if we allow a group to use the nodes of other agents or only their own nodes. We then build axiomatizations built on these properties. While the two solutions are usually seen as competitors in the private approach, the results point towards a different interpretation: the two solutions are based on different interpretations of the mcst problem, but are otherwise conceptually very close.
    Keywords: Minimum cost spanning tree; value sharing; cycle-complete solution; folk solution.
    JEL: C71 D63
    Date: 2021–03
  21. By: Ille, Sebastian
    Abstract: Human cooperation for reasons other than self-interest has long intrigued social scientists leading to a substantial literature in economics. Its complement –sectarianism – has not received closer attention in economics despite its significant impact. Based on a dynamic model, the paper shows that sectarianism can be understood as the outcome of a repeated bargaining process in which sectarian affiliation evolves into a pure coordination signal that attributes economic and political benefits. It demonstrates that such sectarian social contracts co-evolve with the sects’ degree of coerciveness and are self-reinforcing. Sectarian conflict may then not be a result of diverging religious ideologies but is shown to be caused by external manipulations of the signal (e.g. via identity politics), and internal political and economic grievances within a sect that spill over to the inter-sectarian level while adopting a sectarian appearance. Theoretical results are supported by empirical findings from the Middle East.
    Keywords: Sectarianism Cooperation, Evolutionary game theory, Agent-based modelling
    JEL: C61 C7 C73 D74 P48 Z1
    Date: 2021–01–18
  22. By: Zack Dorner (University of Waikato); Steven Tucker (University of Waikato); Gazi Hassan (University of Waikato)
    Abstract: The linear public goods game with a voluntary contribution mechanism (VCM) has a large literature providing many insights for the field. Recent papers have investigated impacts on contributions of heterogeneity, risk and ambiguity in marginal per capita return (MPCR) from the public good. We investigate a neglected, but highly relevant set up. In our experiment, the voluntary contribution of one individual to the public good may be more/less productive than another, and this productivity may be uncertain or ambiguous. We have four treatments: HOMOGENOUS (all members of the fixed groups of four are of equal productivity), CERTAIN (two high productivity, two low, but randomly switching in future periods), UNCERTAIN (each subject has a 50-50 lottery of being high or low productivity) and AMBIGUOUS (each subject has an unknown probability of being high or low). High productivity subjects contribute more in the CERTAIN treatment. We find contribution levels are stable in the three treatments over the 10 periods, whereas contributions in the HOMOGENOUS control decline as per the standard finding in a public goods game. These results suggest a natural veil of ignorance about current or future individual productivity, and a social norm of the highly productive contributing more, support a more stable level of contributions over time. Our results are relevant to many field examples, such as contributing to the public good by wearing a face mask in a pandemic, given it is uncertain/ambiguous whether the wearer is contagious (high productivity) or not (low productivity).
    Keywords: ambiguity; heterogeneous productivity; public goods game; social norms; uncertainty; voluntary contribution mechanism
    JEL: C92 D62 D63 D64 H41
    Date: 2021–03–08
  23. By: James A. Brander; Barbara J. Spencer
    Abstract: This paper examines intellectual property litigation as a method of protection from patent-infringing imports. Claims against patent-infringing imports entering the United States may be filed before the International Trade Commission (ITC) or in district court. The ITC applies injunctions (import prohibitions) that would seem to provide more protection from infringing imports than the standard license fee remedy in court. Settlements prior to legal adjudication are common in both venues. Using a model with Nash bargaining and Cournot competition, we show that an ITC filing may restrict imports by less than in court. This result tends to apply if product differentiation is high and the size of the patented cost-reducing innovation is large.
    JEL: C70 F12 F13 K41 O34
    Date: 2021–02
  24. By: Nicolas Quérou; Agnes Tomini; Christopher Costello
    Abstract: We analyze theoretically an institution called a “limited-tenure concession” for its ability to induce efficient public goods contribution and common-pool resource extraction. The basic idea is that by limiting the tenure over which an agent can enjoy the public good, but offering the possibility of renewal contingent on ample private provision of that good, efficient provision may be induced. We first show in a simple repeated game setting that limited-tenure concessions can incentivize socially-efficient provision of public goods. We then analyze the ability of this instrument to incentivize the first best provision for common-pool natural resources such as fish and water, thus accounting for spatial connectivity and natural growth dynamics of the resource. The duration of tenure and the dispersal of the resource play pivotal roles in whether this limited-duration concession induces the socially optimal private provision. Finally, in a setting with costly monitoring, we discuss the features of a concession contract that ensure first-best behavior, but at least cost to the implementing agency.
    JEL: H41 Q2
    Date: 2021–02

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