nep-gth New Economics Papers
on Game Theory
Issue of 2020‒08‒24
twenty-two papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Characterization of TU games with stable cores by nested balancedness By Michel Grabisch; Peter Sudhölter
  2. Imperfect Information, Social Norms, and Beliefs in Networks By Rapanos, Theodoros; Sommer, Marc; Zenou, Yves
  3. Optimal Relevance in Imperfect Information Games By Jorge Miguel Streb
  4. Generating Empirical Core Size Distributions of Hedonic Games using a Monte Carlo Method By Andrew J. Collins; Sheida Etemadidavan; Wael Khallouli
  5. Overcoming Free-Riding in Bandit Games By Hörner, Johannes; Klein, Nicolas; Rady, Sven
  6. Wage Bargaining and Employment Revisited: Separability and Efficiency in Collective Bargaining By Claus-Jochen Haake; Thorsten Upmann; Papatya Duman
  7. Naivete and Sophistication in Initial and Repeated Play in Games By Garcia-Pola, Bernardo; Iriberri, Nagore
  8. The Market for Lemons with Seller Partition By Gersbach, Hans; Mamageishvili, Akaki; Tejada, Oriol
  9. Endogenous Group Formation and its impact on Cooperation and Surplus Allocation - An Experimental Analysis By Di Guida, Sibilla; Han, The Anh; Kirchsteiger, Georg; Lenaerts, Tom; Zisis, Ioannis
  10. Distributionally Robust Pricing in Independent Private Value Auctions By Alex Suzdaltsev
  11. Pricing group membership By Siddhartha Bandyopadhyay; Antonio Cabrales
  12. Relative wealth concerns with partial information and heterogeneous priors By Chao Deng; Xizhi Su; Chao Zhou
  13. Only Time Will Tell: Credible Dynamic Signaling By Egor Starkov
  14. Unpacking moral wiggle room: Information preferences and not information itself predict generosity By Danae Arroyos-Calvera; Rebecca McDonald; Daniel Read; Bruce Rigal
  15. How Altruistic Is Indirect Reciprocity? - Evidence from Gift-Exchange Games in the Lab By Johannes Becker; Daniel Hopp; Karolin Süß
  16. The Political Economy of Reconciliation: A Theoretical Primer By Atin Basuchoudhary; Andreas Freytag
  18. Games with unobservable heterogeneity and multiple equilibria: An application to mobile telecommunications By Mathieu Marcoux
  19. Robust utility maximization under model uncertainty via a penalization approach By Ivan Guo; Nicolas Langrené; Gregoire Loeper; Wei Ning
  20. The perils of democracy By Gregory de Angelo; Dimitri Dubois; Rustam Romaniuc
  21. Fine Cartels By David K Levine
  22. Bargaining over Mandatory Spending and Entitlements By Marina Azzimonti; Gabriel P. Mihalache; Laura Karpuska

  1. By: Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics Université Paris 1 Panthéon-Sorbonne); Peter Sudhölter (COHERE, University of Southern Denmark)
    Abstract: A balanced utility game (N,v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out that outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable
    Keywords: Domination; stable set; core; TU game
    JEL: C71
    Date: 2020–06
  2. By: Rapanos, Theodoros; Sommer, Marc; Zenou, Yves
    Abstract: We develop a simple Bayesian network game in which players, embedded in a network of social interactions, bear a cost from deviating from the social norm of their peers. All agents face uncertainty about the private benefits and the private and social costs of their actions. We prove the existence and uniqueness of a Bayesian Nash equilibrium and characterize players' optimal actions. We then show that denser networks do not necessary increase agents' actions and welfare. We also find that, in some cases, it is optimal for the planner to affect the payoffs of selected individuals rather than all agents in the network. We finally show that having more information is not always beneficial to agents and can, in fact, reduce their welfare. We illustrate all our results in the context of criminal networks in which offenders do not know with certitude the probability of being caught and do not want to be different from their peers in terms of criminal activities.
    Keywords: Bayesian games; beliefs; Conformism; crime; networks; value of information
    JEL: C72 D82 D85 K42
    Date: 2019–10
  3. By: Jorge Miguel Streb
    Abstract: I analyze how natural language transmits information about the sender’s intended actions, complementing previous work on sender-receiver games where natural language transmits information about the sender’s type. Unlike solution concepts based on Nash equilibria, here the solution concept takes into account that when language is used as a signal, a message’s literal meaning may convey common understandings. I incorporate the semantic feature that only a shared natural language is comprehensible, but the equilibrium meaning depends on the strategic context because the credibility of the message depends on the sender’s incentives to be truthful. This setup can be interpreted as a formal pragmatics, i.e., as a setup that studies the actual use of language in specific games. Words are not proof of what they state, so mistrust equilibria are always possible. In trust equilibria, the sender aims at optimal relevance.
    Keywords: asymmetric information, unilateral communication, conventional signs, semantics, pragmatics
    JEL: D83 C72
    Date: 2019–11
  4. By: Andrew J. Collins; Sheida Etemadidavan; Wael Khallouli
    Abstract: Data analytics allows an analyst to gain insight into underlying populations through the use of various computational approaches, including Monte Carlo methods. This paper discusses an approach to apply Monte Carlo methods to hedonic games. Hedonic games have gain popularity over the last two decades leading to several research articles that are concerned with the necessary, sufficient, or both conditions of the existence of a core partition. Researchers have used analytical methods for this work. We propose that using a numerical approach will give insights that might not be available through current analytical methods. In this paper, we describe an approach to representing hedonic games, with strict preferences, in a matrix form that can easily be generated; that is, a hedonic game with randomly generated preferences for each player. Using this generative approach, we were able to create and solve, i.e., find any core partitions, of millions of hedonic games. Our Monte Carlo experiment generated games with up to thirteen players. The results discuss the distribution form of the core size of the games of a given number of players. We also discuss computational considerations. Our numerical study of hedonic games gives insight into the underlying properties of hedonic games.
    Date: 2020–07
  5. By: Hörner, Johannes; Klein, Nicolas; Rady, Sven
    Abstract: This paper considers a class of experimentation games with Lévy bandits encompassing those of Bolton and Harris (1999) and Keller, Rady and Cripps (2005). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players' payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (MPE). This is not an artifact of continuous time: we prove that such equilibria arise as limits of equilibria in the discrete-time game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium.
    Keywords: Bayesian learning; strategic experimentation; Strongly Symmetric Equilibrium; Two-Armed Bandit
    JEL: C73 D83
    Date: 2019–10
  6. By: Claus-Jochen Haake; Thorsten Upmann; Papatya Duman
    Abstract: We analyse the two-dimensional Nash bargaining solution (NBS) deploying a standard labour market negotiations model (McDonald and Solow, 1981). We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems such that the two solutions together replicate the solution of the two-dimensional problem, if the NBS is applied. The axiom of Independence of Irrelevant Alternatives turns out to be crucial for decomposability. Our result has significant implications for actual negotiations, as it allows for the decomposition of a multi-dimensional bargaining problem into simpler problems—and thus helps to facilitate real-world negotiations.
    Keywords: labour market negotiations, efficient bargains, Nash bargaining solution, sequential bargaining, restricted bargaining games
    JEL: J52 J41 C78
    Date: 2020
  7. By: Garcia-Pola, Bernardo; Iriberri, Nagore
    Abstract: Naive, non-equilibrium, behavioral rules, compared to more sophisticated equilibrium theory, are often better in describing individuals' initial play in games. Additionally, in repeated play in games, when individuals have the oppor- tunity to learn about their opponents' past behavior, learning models of different sophistication levels are successful in explaining how individuals modify their behavior in response to feedback. How do subjects following different behavioral rules in initial play modify their behavior after learning about past behavior? This study links both initial and repeated play in games, analyzing elicited behavior in 3x3 normal-form games using a within-subject laboratory design. We classify individuals into different behavioral rules in both initial and repeated play and test whether and/or how naivete and sophistication in initial play correlates with naivete and sophistication in repeated play. We find no evidence for a correlation between naivete and sophistication in initial and repeated play.
    Keywords: adaptive and sophisticated learning; initial play; level-k thinking; mixture-of-types estimation; Naivete; repeated play; Sophistication
    JEL: C70 C91 C92
    Date: 2019–10
  8. By: Gersbach, Hans; Mamageishvili, Akaki; Tejada, Oriol
    Abstract: We introduce a four-stage, multi-prize buying mechanism, which can be used by a (big) buyer to separate low-quality sellers, called "lemon" owners, from high-quality sellers. When the pool of sellers can be partitioned into groups with known mixes of high- and low-quality sellers, the buyer obtains the commodities from the high-quality sellers at a price that matches the willingness to sell. By contrast, "lemon" owners are trapped into selling their items at a low, or even negligible, price. These properties hold even if the buyer cannot commit to a single execution of the mechanism. We outline some applications of our results and suggest that our mechanism might be useful for market makers.
    Keywords: Lemons market - Partition - Signaling - Commitment - Decoy ballots
    JEL: C72 D4 D82 D86
    Date: 2019–10
  9. By: Di Guida, Sibilla (Department of Business and Economics); Han, The Anh (School of Computing); Kirchsteiger, Georg (ECARES); Lenaerts, Tom (Vrije Universiteit Brussel); Zisis, Ioannis (MLG)
    Abstract: This paper investigates how endogenous group formation combined with the possibility of repeated interaction impacts cooperation within groups and surplus distribution. We developed and tested experimentally a Surplus Allocation Game where cooperation of four agents is needed to produce surplus, but only two have the power to allocate it among the group members. Different matching procedures were used to test the impact of exogenous vs. endogenous group formation. Our results show that repeated interaction with the same partners (endogenous group formation) leads to a self-selection of agents into groups with different life-spans, whose duration is correlated with the behavior of both distributors and receivers. While behavior at the group level is diverse for surplus allocation and amount of cooperation, aggregate behavior is instead similar when groups are exogenously or endogenously formed. Our results cast doubts whether the possibility of repeated interaction can lead to cooperation and efficient outcomes when the ex-post bargaining power about the surplus distribution is very unequal. Rather, it seems to amplify differences in the cooperation and distribution behavior across groups.
    Keywords: Cooperation; surplus distribution; exogenous group formation; endogenous group formation
    JEL: C72 C92 D03
    Date: 2020–08–20
  10. By: Alex Suzdaltsev
    Abstract: A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. We prove that it is always optimal to set the reserve price to seller's own valuation. However, the maxmin reserve price may not be unique. If the number of bidders is sufficiently high, all prices below the seller's valuation, including zero, are also optimal. A second-price auction with the reserve equal to seller's value (or zero) is an asymptotically optimal mechanism (among all mechanisms) as the number of bidders grows without bound.
    Date: 2020–08
  11. By: Siddhartha Bandyopadhyay (University of Birmingham); Antonio Cabrales (University College London)
    Abstract: We consider a model where agents differ in their 'types' which determines their voluntary contribution towards a public good. We analyze what the equilibrium composition of groups are under centralized and centralized choice. We show that there exists a top-down sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by level of types, with the first k types in the group with the highest price and so on. This exists both under decentralized and centralized choosing. We also analyze the model with endogenous group size and examine under what conditions is top-down sorting socially effcient. We illustrate when integration (i.e. mixing types so that each group's average type if the same) is socially better than top-down sorting. Finally, we show that top down sorting is efficient even when groups compete among themselves.
    Keywords: Top down sorting, Group formation, Public good, Segregation, Integration.
    JEL: D02 D64 D71 H41
    Date: 2020–08
  12. By: Chao Deng; Xizhi Su; Chao Zhou
    Abstract: We establish a Nash equilibrium in a market with $ N $ agents with the performance criteria of relative wealth level when the market return is unobservable. Each investor has a random prior belief on the return rate of the risky asset. The investors can be heterogeneous in both the mean and variance of the prior. By a separation result and a martingale argument, we show that the optimal investment strategy under a stochastic return rate model can be characterized by a fully-coupled linear FBSDE. Two sets of deep neural networks are used for the numerical computation to first find each investor's estimate of the mean return rate and then solve the FBSDEs. We establish the existence and uniqueness result for the class of FBSDEs with stochastic coefficients and solve the utility game under partial information using deep neural network function approximators. We demonstrate the efficiency and accuracy by a base-case comparison with the solution from the finite difference scheme in the linear case and apply the algorithm to the general case of nonlinear hidden variable process. Simulations of investment strategies show a herd effect that investors trade more aggressively under relativeness concerns. Statistical properties of the investment strategies and the portfolio performance, including the Sharpe ratios and the Variance Risk ratios (VRRs) are examed. We observe that the agent with the most accurate prior estimate is likely to lead the herd, and the effect of competition on heterogeneous agents varies more with market characteristics compared to the homogeneous case.
    Date: 2020–07
  13. By: Egor Starkov (Department of Economics, University of Copenhagen, Denmark)
    Abstract: This paper explores a model of dynamic signaling without commitment. It is known that separating equilibria do not exist if the sender cannot commit to future costly actions, since no single action can have enough weight to be an effective signal. This paper, however, shows that informative and payoff-relevant signaling can occur even without commitment and without resorting to unreasonable off-path beliefs. Such signaling can only happen through attrition, when the weakest type mixes between revealing own type and pooling with the stronger types. The possibility of full information revelation in the limit hence depends crucially on the assumptions about the state space. We illustrate the results by exploring a model of dynamic price signaling and show that prices may be informative of product quality even if the seller cannot commit to future prices, with both high and low prices being able to signal high quality.
    Keywords: dynamic signaling, repeated signaling, reputation, attrition
    JEL: C73 D82 D83 L15
    Date: 2020–08
  14. By: Danae Arroyos-Calvera (University of Birmingham); Rebecca McDonald (University of Birmingham); Daniel Read (University of Warwick); Bruce Rigal (St Mary's University)
    Abstract: It has been suggested that avoiding information provides people with moral wiggle room to behave less pro-socially. In a novel dictator game context we unpack the effect of moral wiggle room along two dimensions: whether information is hidden from the recipient or the dictator; and whether generosity is influenced by the information condition, or whether, instead, less generous types self-select into hidden information states. Participants (n=1,360) play a lottery dictator game with three treatments differing in who knows and does not know the endowment (the information state) and - importantly - whether the information state is exogenously or endogenously determined. We found that it was the information state dictators preferred, not the information state they eventually received, that could predict generosity. Dictators who preferred to hide information from the recipient were the least likely to make a generous transfer, and those who preferred to hide information from themselves were more likely to make a generous transfer.
    Keywords: Self-image; Social-image; Self-Selection; Moral Wiggle Room; Information.
    Date: 2020–08
  15. By: Johannes Becker; Daniel Hopp; Karolin Süß
    Abstract: Indirect reciprocity is defined as a specific kind of behavior: An agent rewards or penalizes another agent for having behaved kindly or unkindly toward a third party. This paper analyzes the question of what drives indirect reciprocity: Does the agent reward or penalize because she (altruistically) cares for the third party? Or does she take the other agent’s behavior as a signal of how the latter would treat her if they met? In order to measure the relative importance of the altruism motive versus the signaling motive, we consider a gift-exchange game with three players: an employer pays wages to a worker and a coworker, before the worker (but not the coworker) may reciprocate by exerting effort. We offer a theoretical framework to analyze both motives for indirect reciprocity and run a series of lab experiments. The treatments manipulate the worker’s information on wages. We find that, if only the coworker’s wage is observable, the worker’s effort increases in the coworker’s wage. In contrast, if the worker can observe her own wage, the coworker’s wage does not affect worker effort at all. We interpret this as support for the signaling motive: Indirect reciprocity is rather a byproduct of direct reciprocity than an act of altruism.
    Keywords: gift-exchange, indirect reciprocity, signaling
    JEL: A13 C92 D91 J31
    Date: 2020
  16. By: Atin Basuchoudhary; Andreas Freytag
    Abstract: Conflicts end. Often though, the roots of future conflict remain in fertile soil. The process of reconciliation among erstwhile enemies may be a way to deter future conflagrations; we have witnessed a number of examples such as in Rwanda or South Africa. However, to be sustainable and effective, this process may require cultural change. We use evolutionary game theory to model this process of cultural change. We postulate three cultures in a population – Conciliatory, Non-conciliatory, and Reciprocative. We then use the replicator dynamic to identify evolutionary stable outcomes. People in our population are boundedly rational. They may, therefore, “belong” to a particular culture. However, they learn to adopt other cultures if it is beneficial. We find first that people can learn to be Non-conciliatory even when Conciliation provides very real benefits. However, a population can learn the reciprocative culture to facilitate reconciliation. Whether it does or not depends on the initial distribution of the population among the three cultures and how people feel about the future. These results are well known in the Evolutionary Game Theory literature. However, to our knowledge, this is the first time these results have been applied to provide insights into post-conflict reconciliation processes.
    Keywords: conflict, reconciliation
    JEL: D78 H12
    Date: 2020
  17. By: Irene Crimaldi (IMT Institute for Advanced Studies [Lucca]); Pierre-Yves Louis (LMA-Poitiers - Laboratoire de Mathématiques et Applications - Université de Poitiers - CNRS - Centre National de la Recherche Scientifique); Ida Minelli (UNIVAQ - University of L'Aquila [Italy])
    Abstract: Rich get richer rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.
    Keywords: CODA models,Technological dynamics,Coordination games,Evolutionary-game theory,Stochastic approximation,Reinforcement learning,Generalized Pólya urn,Non-linear Pólya urn,Urn model,Reinforced stochastic process,Interacting stochastic processes,Interacting agents
    Date: 2020–08–01
  18. By: Mathieu Marcoux (Université de Montréal)
    Abstract: To shed light on the limited success of competition enhancing policies in mobile telecommunications, I estimate a game of transceivers’ locations between national incumbents and a new entrant in Canada. I recover player-specific unobserved heterogeneity from bids for spectrum licenses to address the unavailability of regressors required to identify incumbents’ responses to the new entrant’s decisions. I find that incumbents benefitting from important economies of density is a plausible explanation for policies’ drawbacks. I then evaluate the equilibrium effect of subsidizing the new entrant’s transceivers and find that this alternative proposition increases its investments while only slightly modifying incumbents’.
    Keywords: Multiple equilibria, Unobserved heterogeneity, Empirical games, Telecommunications
    JEL: C57 L11
    Date: 2019–02
  19. By: Ivan Guo (Monash University [Melbourne]); Nicolas Langrené (CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra]); Gregoire Loeper (Monash University [Melbourne]); Wei Ning (Monash University [Melbourne])
    Abstract: This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We test this robust algorithm on real market data. The results show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns. To solve for the value function, we derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by three methods: finite difference method, Monte Carlo simulation, and Generative Adversarial Networks.
    Keywords: robust portfolio optimization,differential games,HJBI equation,Generative adversarial networks,GANs,Monte Carlo
    Date: 2020–08–01
  20. By: Gregory de Angelo (Claremont Graduate University [Claremont, CA ]); Dimitri Dubois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Rustam Romaniuc (LEM - Lille économie management - LEM - UMR 9221 - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)
    Abstract: In this work we examine a common social dilemma in experimental economics, the public goods game, to determine how voting impacts pro-social behavior. As noted in Markussen et al. (2014), a democratic dividend exists. Couching the public goods game in a phenomenon that is playing out in much of the world – drastic income inequality – we examine the decision of groups to share local public goods with groups that have, effectively, no endowment to contribute toward public nor private consumption. Our results show the perils of democracy in that subjects in the position to vote use their advantageous situation to reward the ingroups at the expense of the less endowed outgroup members.
    Date: 2020
  21. By: David K Levine
    Date: 2020–08–04
  22. By: Marina Azzimonti; Gabriel P. Mihalache; Laura Karpuska
    Abstract: Do mandatory spending rules improve social welfare? We analyze a dynamic political-economy model in which two parties disagree on the split of a fixed budget between public goods and private transfers. Under a mandatory spending rule, expenditures are governed by criteria set by enacted law, namely last year’s spending bill is applied in the current year unless successfully changed by a majority of policymakers. We model budget rules with an endogenous status quo and study the welfare implications of introducing entitlement programs. Entitlements depend on individual eligibility and participation and, hence, impose constraints on publicly-provided private goods and transfers. We emphasize that bargaining over entitlements is qualitatively different from bargaining over public goods provision, particularly with risk-aversion. Entitlement programs induce under-provision of public goods but also a smoother path for private consumption than discretion. Whether entitlement programs are welfare-improving depends critically on political turnover. When proposers alternate frequently, it benefits society because it reduces volatility in private consumption. Outcomes under rules can be worse than under discretion if political power is persistent enough. We contrast these findings to those from a mandatory spending rule on public goods, commonly studied in the literature. Finally, we describe conditions under which all parties would agree to the introduction of budget rules, within a bargaining equilibrium.
    JEL: C7 D6 E6 E62 H53
    Date: 2020–07

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