nep-gth New Economics Papers
on Game Theory
Issue of 2021‒04‒12
nineteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Games on Endogenous Networks By Benjamin Golub; Evan Sadler
  2. Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium By Claus-Jochen Haake; Walter Trockel
  3. Evolutionary Strategies with Analogy Partitions in p-guessing Games By Aymeric Vie
  4. Sharing the cost of cleaning up a polluted river By Wenzhong Li; Genjiu Xu; Rene van den Brink
  5. Strategic justifications of the TAL-family of rules for bankruptcy problems By Juan D. Moreno-Ternero; Min-Hung Tsay; Chun-Hsien Yeh
  6. Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction By García-Martínez, Jose A.; Mayor-Serra, Antonio J.; Meca, Ana
  7. A Genetic Algorithm approach to Asymmetrical Blotto Games with Heterogeneous Valuations By Aymeric Vie
  8. Treating Symmetric Buyers Asymmetrically By Banerjee, Shraman
  9. Mathematical indices for the influence of risk factors on the lethality of a disease By Ricardo Martínez; Joaquín Sánchez-Soriano
  10. Competitive Nonlinear Pricing under Adverse Selection By Attar, Andrea; Mariotti, Thomas; Salanié, François
  11. On Determining Leading Coalitions in Supply Chains: Methodology and Application By Kidd, Martin P.; Borm, Peter
  12. Common pool resource management and risk perceptions By Can Askan Mavi; Nicolas Quérou
  13. Prisoner Dilemma in maximization constrained: the rationality of cooperation By Mahdi HajiAliAkbari; Shahin Esmaeili
  14. Beliefs asymmetry and price stability in a cobweb model By Berardi, Michele
  15. Rationality and Emotions: A Model of Inner Games and Ego Identity By Liu, Fen
  16. Robust double auction mechanisms By Kiho Yoon
  17. Coevolution of actions, personal norms, and beliefs about others in social dilemmas By Gavrilets, Sergey
  18. A Search and Bargaining Model of Non-degenerate Distributions of Money Holdings By Kazuya Kamiya; So Kubota
  19. Cartel Stability in Times of Low Interest Rates By Severin Lenhard

  1. By: Benjamin Golub; Evan Sadler
    Abstract: We study network games in which players both create spillovers for one another and choose with whom to associate. The endogenous outcomes include both the strategic actions (e.g., effort levels) and the network in which spillovers occur. We introduce a framework and two solution concepts that extend standard approaches -- Nash equilibrium in actions and pairwise (Nash) stability in links. Our main results show that under suitable monotonicity assumptions on incentives, stable networks take simple forms. Our central conditions concern whether actions and links are strategic complements or substitutes, as well as whether links create positive or negative payoff spillovers. 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.
    Date: 2021–02
  2. By: Claus-Jochen Haake (Paderborn University); Walter Trockel (Bielefeld University)
    Abstract: In this article we combine Debreu's (1952) social system with Hurwicz's (1994, 2008) ideas of embedding a "desired" game form into a "natural" game form that includes all feasible behavior, even if it is "illegal" according to the desired form. For the resulting socio-legal system we extend Debreu's concepts of a social system and its social equilibria to a socio-legal system with its Debreu-Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (1975) that also generalizes the dc-mechanism of Koray and Yildiz (2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two-person cooperative bargaining. There we provide in a socio-legal system based on Nash's demand game an implementation of the Nash bargaining solution in Debreu-Hurwicz equilibrium.
    Keywords: socio-legal systems, implementation, social systems, generalized games, Nash demand game
    JEL: D02 C78 C72
    Date: 2021–04
  3. By: Aymeric Vie
    Abstract: In Keynesian Beauty Contests notably modeled by p-guessing games, players try to guess the average of guesses multiplied by p. Convergence of plays to Nash equilibrium has often been justified by agents' learning. However, interrogations remain on the origin of reasoning types and equilibrium behavior when learning takes place in unstable environments. When successive values of p can take values above and below 1, bounded rational agents may learn about their environment through simplified representations of the game, reasoning with analogies and constructing expectations about the behavior of other players. We introduce an evolutionary process of learning to investigate the dynamics of learning and the resulting optimal strategies in unstable p-guessing games environments with analogy partitions. As a validation of the approach, we first show that our genetic algorithm behaves consistently with previous results in persistent environments, converging to the Nash equilibrium. We characterize strategic behavior in mixed regimes with unstable values of p. Varying the number of iterations given to the genetic algorithm to learn about the game replicates the behavior of agents with different levels of reasoning of the level k approach. This evolutionary process hence proposes a learning foundation for endogenizing existence and transitions between levels of reasoning in cognitive hierarchy models.
    Date: 2021–03
  4. By: Wenzhong Li (Northwestern Polytechnical University); Genjiu Xu (Northwestern Polytechnical University); Rene van den Brink (Vrije Universiteit Amsterdam)
    Abstract: Consider a group of agents located along a polluted river where every agent must pay a certain cost for cleaning up the polluted river. Following the model of Ni and Wang (2007), we propose the class of alpha-Local Responsibility Sharing methods, which generalizes the Local Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. We fi rst show that the UES method is characterized by relaxing independence of upstream costs appearing in Ni and Wang (2007). Then we provide two axiomatizations with endogenous responsibility of the alpha-Local Responsibility Sharing method, one using this weak independence axiom (taken from the UES method) and one using a weak version of the no blind cost axiom (taken from the LRS method). Moreover, we also provide an axiomatization with exogenous responsibility by introducing alpha-responsibility balance. Finally, we defi ne a pollution cost-sharing game, and show that, interestingly, the Half Local Responsibility Sharing (HLRS) method coincides with the Shapley value, the nucleolus and the tau-value of the corresponding pollution cost-sharing game. This HLRS method can be seen as some kind of middle compromise of the LRS and UES methods.
    Keywords: pollution cost-sharing problems, alpha-Local Responsibility Sharing method, axiomatization, cooperative games
    JEL: Q53 C71 Q25
    Date: 2021–04–05
  5. By: Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;); Min-Hung Tsay (Department of Economics, National Chung Cheng University); Chun-Hsien Yeh (Institute of Economics, Academia Sinica; Chung-Hua Institute for Economic Research)
    Abstract: We follow the Nash program to provide a new strategic justification for the TAL-family of rules for bankruptcy problems. The design of our game is inspired by an axiomatization of the TAL-family of rules exploiting the properties of consistency together with certain degrees of lower and upper bounds to all creditors. Bilateral negotiations of our game follow the spirit of those bounds. By means of consistency, we then extend the bilateral negotiations to an arbitrary number of creditors.
    Keywords: Nash program; bankruptcy problems; strategic justification; consistency; TAL-family of rules
    JEL: C71 C72 D63
    Date: 2021
  6. By: García-Martínez, Jose A.; Mayor-Serra, Antonio J.; Meca, Ana
    Abstract: There are multiple situations in which bilateral interaction between agents results in considerable cost reductions. Such interaction can occur in settings where agents are interested in sharing resources, knowledge or infrastructures. Their common purpose is to obtain individual advantages, e.g. by reducing their respective individual costs. Achieving this pairwise cooperation often requires the agents involved to make some level of effort. It is natural to think that the amount by which one agent could reduce the costs of the other may depend on how much effort the latter exerts. In the first stage, agents decide how much effort they are to exert, which has a direct impact on their pairwise cost reductions. We model this first stage as a non-cooperative game, in which agents determine the level of pairwise effort to reduce the cost of their partners. In the second stage, agents engage in a bilateral interaction between independent partners. We study this bilateral cooperation as a cooperative game in which agents reduce each other's costs as a result of cooperation, so that the total reduction in the cost of each agent in a coalition is the sum of the reductions generated by the rest of the members of that coalition. In the non-cooperative game that precedes cooperation with pairwise cost reduction, the agents anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of the effort exerted into their cost functions. Based on this model, we explore the costs, benefits, and challenges associated with setting up a pairwise effort network. We identify a family of cost allocations with weighted pairwise reduction which are always feasible in the cooperative game and contain the Shapley value. We show that there are always cost allocations with weighted pairwise reductions that generate an optimal level of efficient effort and provide a procedure for finding the efficient effort equilibrium.
    Keywords: Allocation, Cost models, Efficiency, Game Theory
    JEL: C71 C72
    Date: 2020–12–15
  7. By: Aymeric Vie
    Abstract: Blotto Games are a popular model of multi-dimensional strategic resource allocation. Two players allocate resources in different battlefields in an auction setting. While competition with equal budgets is well understood, little is known about strategic behavior under asymmetry of resources. We introduce a genetic algorithm, a search heuristic inspired from biological evolution, interpreted as social learning, to solve this problem. Most performant strategies are combined to create more performant strategies. Mutations allow the algorithm to efficiently scan the space of possible strategies, and consider a wide diversity of deviations. We show that our genetic algorithm converges to the analytical Nash equilibrium of the symmetric Blotto game. We present the solution concept it provides for asymmetrical Blotto games. It notably sees the emergence of "guerilla warfare" strategies, consistent with empirical and experimental findings. The player with less resources learns to concentrate its resources to compensate for the asymmetry of competition. When players value battlefields heterogeneously, counter strategies and bidding focus is obtained in equilibrium. These features are consistent with empirical and experimental findings, and provide a learning foundation for their existence.
    Date: 2021–03
  8. By: Banerjee, Shraman
    Abstract: We investigate a finite-horizon dynamic pricing problem of a seller under limited commitment. Even when the buyers are ex-ante symmetric to the seller, the seller can charge different prices to different buyers. We show that under the class of posted-price mechanisms this asymmetric treatment of symmetric buyers strictly revenue-dominates symmetric treatment. The seller im- plements this by using a priority-based deterministic tie-breaking rule instead of using a random tie-breaking rule. The effect of asymmetric treatment on revenue increment increases monotonically as we increase the time horizon of the game.
    Keywords: Dynamic Pricing, Asymmetric Mechanism, Non-Anonymity
    JEL: C70 D42 D44 D82
    Date: 2021–01–11
  9. By: Ricardo Martínez (Department of Economic Theory and Economic History, University of Granada.); Joaquín Sánchez-Soriano (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche.)
    Abstract: We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.
    Keywords: Epidemiology, Comorbidity, Lethality, Equal attribution index, Shapley value index, COVID-19.
    Date: 2021–03–28
  10. By: Attar, Andrea; Mariotti, Thomas; Salanié, François
    Abstract: This article surveys recent attempts at characterizing competitive allocations under adverse selection when each informed agent can privately trade with several uninformed parties: that is, trade is nonexclusive. We rst show that requiring market outcomes to be robust to entry selects a unique candidate allocation, which involves cross-subsidies. We then study how to implement this allocation as the equilibrium outcome of a game in which the uninformed parties, acting as principals, compete by making oers to the informed agents. We show that equilibria typically fail to exist in competitive- screening games, in which these oers are simultaneous. We nally explore alternative extensive forms, and show that the candidate allocation can be implemented through a discriminatory ascending auction. These results yield sharp predictions for competitive nonexclusive markets.
    Keywords: Adverse Selection; Entry-Proofness; Discriminatory Pricing; Nonexclusive; Markets; Ascending Auctions
    JEL: D43 D82 D86
    Date: 2021–04
  11. By: Kidd, Martin P.; Borm, Peter (Tilburg University, Center For Economic Research)
    Keywords: Supply chain collaboration; Cooperative bargaining; Nucleolus selections; Linear production processes
    Date: 2021
  12. By: Can Askan Mavi (Department of Economics and Management, Université du Luxembourg); Nicolas Quérou (CEE-M, Université de Montpellier, FR)
    Abstract: Motivated by recent discussions about the issue of risk perceptions for climate change related events, we introduce a non-cooperative game setting where agents manage a common pool resource under a potential risk, and agents exhibit different risk perception biases. Focusing on the effect of the polarization level and other population features, we show that the type of bias (overestimation versus underestimation biases) and the resource quality level before and after the occurrence of the shift have first-order importance on the qualitative nature of behavioral adjustments and on the pattern of resource conservation. When there are non-uniform biases within the population, the intra-group structure of the population qualitatively affects the degree of resource conservation. Moreover, unbiased agents may react in nonmonotone ways to changes in the polarization level when faced with agents exhibiting different types of bias. The size of the unbiased agents’ sub-population does not qualitatively affect how an increase in the polarization level impacts individual behavioral adjustments, even though it affects the magnitude of this change. Finally, it is shown how perception biases affect the comparison between centralized and decentralized management.
    Keywords: Conservation, Perception bias, Environmental risk, Renewable resources, Dynamic games.
    JEL: Q20 Q54 D91 C72
    Date: 2020
  13. By: Mahdi HajiAliAkbari; Shahin Esmaeili
    Abstract: David Gauthier in his article, Maximization constrained: the rationality of cooperation, tries to defend the joint strategy in situations in which no outcome is both equilibrium and optimal. Prisoner Dilemma is the most familiar example of these situations. He first starts with some quotes by Hobbes in Leviathan; Hobbes, in chapter 15 discusses an objection by someone is called Foole, and then will reject his view. In response to Foole, Hobbes presents two strategies (i.e. joint and individual) and two kinds of agents in such problems including Prisoner Dilemma, i.e. straightforward maximizer (SM) and constrained maximizer(CM). Then he considers two arguments respectively for SM and CM, and he will show that why in an ideal and transparent situation, the first argument fails and the second one would be the only valid argument. Likewise, in the following part of his article, he considers more realistic situations with translucency and he concludes that under some conditions, the joint strategy would be still the rational decision.
    Date: 2021–02
  14. By: Berardi, Michele
    Abstract: This work analyses the role of asymmetry in beliefs for price dynamics in a cobweb model with heterogeneous expectations and evolutionary selection of predictors. While heterogeneous but symmetric beliefs result in the rational expectations equilibrium price, the effect of asymmetry depends on whether predictors on one side or the other of rationality have a larger support. A support skewed towards predictors that are anchored to past prices can be destabilizing, and the interaction with the evolutionary selection mechanism can lead to complex dynamics in prices; a support skewed towards predictors that overshoot price changes leads instead to price stability, irrespective of the underlying evolutionary dynamics. The design of the set of beliefs allowed to compete on the market is thus crucial for the possible outcomes of the model. One could interpret a skewed support in terms of sentiments, intended as one-sided systematic biases in expectations.
    Keywords: expectations; heterogeneity; evolutionary learning; sentiments.
    JEL: C62 D83 D84 E32
    Date: 2021–03–31
  15. By: Liu, Fen
    Abstract: This paper develops a framework of Inner Games with Ego Identity to discuss an individual’s rationality and emotions in decision making. Following previous efforts of taking psychological insights into economics, this paper dives into the multi-faceted human psychology and proposes a new framework of the decision maker’s Inner Games with Ego Identity in the context of a relationship, and integrates the components of beliefs about oneself and the other one in a relationship into the structure. Moreover, I assume that individuals are motivated mainly by their Ego Identity other than by direct pleasure from consumption, and the utility is derived from the inner state at the moment of decision making. As an application, I define and understand emotions in the framework, such as anger, guilt, and disappointment. For example, I distinguish five types of anger, such as healthy anger to protect one’s personal boundary, and anger to threaten others for some purpose. I end with a discussion of several directions for future research.
    Keywords: Bounded Rationality; Full Rationality; Psychological Game; Emotion
    JEL: C79 D03
    Date: 2021–01–05
  16. By: Kiho Yoon
    Abstract: We study the robust double auction mechanisms, that is, the double auction mechanisms that satisfy dominant strategy incentive compatibility, ex-post individual rationality, ex-post budget balance and feasibility. We first establish that the price in any deterministic robust mechanism does not depend on the valuations of the trading players. We next establish that, with the non-bossiness assumption, the price in any deterministic robust mechanism does not depend on players' valuations at all, whether trading or non-trading, i.e., the price is posted in advance. Our main result is a characterization result that, with the non-bossiness assumption along with other assumptions on the properties of the mechanism, the posted price mechanism with an exogenous rationing rule is the only deterministic robust double auction mechanism. We also show that, even without the non-bossiness assumption, it is quite difficult to find a reasonable robust double auction mechanism other than the posted price mechanism with rationing.
    Date: 2021–02
  17. By: Gavrilets, Sergey
    Abstract: Human decision-making is affected by a diversity of factors including material cost-benefit considerations, normative and cultural influences, learning, and conformity with peers and external authorities (e.g., cultural, religious, political, organizational). Also important are their dynamically changing personal perception of the situation and beliefs about actions and expectations of others as well as psychological phenomena such as cognitive dissonance, and social projection. To better understand these processes, I develop a modeling framework describing the joint dynamics of actions and attitudes of individuals and their beliefs about actions and attitudes of their group-mates. I consider which norms get internalized and which factors control beliefs about others. I predict that the long-term average characteristics of groups are largely determined by a balance between material payoffs and the values promoted by the external authority. Variation around these averages largely reflects variation in individual costs and benefits mediated by individual psychological characteristics. The efforts of an external authority to change the group behavior in a certain direction can, counter-intuitively, have an opposite effect on individual behavior. I consider how various factors can affect differences between groups and societies in tightness/looseness of their social norms. I show that the most important factors are social heterogeneity, societal threat, effects of the authority, cultural variation in the degree of collectivism/individualism, the population size, and the subsistence style. My results can be useful for achieving a better understanding of human social behavior, historical and current social processes, and in developing more efficient policies aiming to modify social behavior
    Date: 2021–04–05
  18. By: Kazuya Kamiya (Research Institute for Economics and Business Administration(RIEB), Kobe University, JAPAN); So Kubota (Faculty of Political Science and Economics, Waseda University)
    Abstract: We study a standard search and bargaining model of money, where goods are traded only in decentralized markets and distributions of money holdings are non-degenerate in equilibria. We assume fixed costs in each seller's production, which allows an analytical characterization of a tractable equilibrium. Each Nash bargaining solution satisfies pay-all property, where the buyer pays the whole amount of cash as a corner solution, and the seller produces goods as the interior solution. In the stationary equilibrium, the aggregate variables, such as total production and the number of matchings, are expressed by given parameters, i.e., determinate. On the other hand, individual-level variables are indeterminate. Distributional monetary policies are e ective in both the short-run and the long-run.
    Date: 2021–03
  19. By: Severin Lenhard
    Abstract: We study the interest rate’s effect on the stability of cartels. A low interest rate implies a high discount factor and thus increases cartel stability. If firms access the capital market, an additional effect comes into play: a low interest rate lowers investment costs, resulting in more profitable deviations from the collusive agreement. We propose a new measure for a cartel’s stability regarding the two opposing effects. Stability is U-shaped in the interest rate. We test our theory using a dataset of 615 firms and find supporting evidence. We conclude that the current unusually low interest rate facilitates collusion.
    Keywords: Collusion, Interest Rate, Repeated Game, Survival Analysis
    JEL: C41 D43 K21 L40
    Date: 2021–03

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