nep-gth New Economics Papers
on Game Theory
Issue of 2022‒09‒26
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Cognitive Hierarchies in Multi-Stage Games of Incomplete Information By Po-Hsuan Lin
  2. Queueing games with an endogenous number of machines By Ata Atay; Christian Trudeau
  3. Investment in the common good: free rider effect and the stability of mixed strategy equilibria By Youngsoo Kim; H. Dharma Kwon
  4. Motives Behind Cooperation in Finitely Repeated Prisoner's Dilemma By Anujit Chakraborty
  5. Two families of values for global games By José María Alonso-Meijide; Mikel à lvarez-Mozos; Maria Gloria Fiestras-Janeiro; Andres Jiménez-Losada
  6. A fundamental Game Theoretic model and approximate global Nash Equilibria computation for European Spot Power Markets By Ioan Alexandru Puiu; Raphael Andreas Hauser
  7. Intrinsic fluctuations of reinforcement learning promote cooperation By Wolfram Barfuss; Janusz Meylahn
  8. Pro-business arbitration with ISDS By Bernard Caillaud; Ariane Lambert-Mogiliansky
  9. Everybody’s Talkin’ at Me: Levels of Majority Language Acquisition by Minority Language Speakers By William Brock; Bo Chen; Steven N. Durlauf; Shlomo Weber
  10. Exit vs. Voice By Broccardo, Eleonora; Hart, Oliver D.; Zingales, Luigi
  11. Competition, Alignment, and Equilibria in Digital Marketplaces By Meena Jagadeesan; Michael I. Jordan; Nika Haghtalab
  12. Care for Elderly Parents: Do Children Cooperate? By Bergeot, J.;
  13. Implementation in vNM Stable Set By Ville Korpela; Michele Lombardi; Riccardo D. Saulle
  14. Public debt and the political economy of reforms By Pierre C. Boyer; Christoph Esslinger; Brian Roberson

  1. By: Po-Hsuan Lin
    Abstract: We explore the dynamic cognitive hierarchy (CH) theory proposed by Lin and Palfrey (2022) in the setting of multi-stage games of incomplete information. In such an environment, players will learn other players' payoff-relevant types and levels of sophistication at the same time as the history unfolds. For a class of two-person dirty faces games, we fully characterize the dynamic CH solution, predicting that lower-level players will figure out their face types in later periods than higher-level players. Finally, we re-analyze the dirty faces game experimental data from Bayer and Chan (2007) and find the dynamic CH solution can better explain the data than the static CH solution.
    Date: 2022–08
  2. By: Ata Atay (University of Barcelona and BEAT); Christian Trudeau (University of Windsor)
    Abstract: This paper studies queueing problems with an endogenous number of machines with and without an initial queue, the novelty being that coalitions not only choose how to queue, but also on how many machines. For a given problem, agents can (de)activate as many machines as they want, at a cost. After minimizing the total cost (processing costs and machine costs), we use a game theoretical approach to share to proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems with an endogenous number of machines, and examine how to share the total cost. We provide an upper bound and a lower bound on the cost of a machine to guarantee the non-emptiness of the core (the set of stable allocations). Next, we study requeueing problems with an endogenous number of machines, where there is an existing queue. We examine how to share the cost savings compared to the initial situation, when optimally requeueing/changing the number of machines. Although, in general, stable allocation may not exist, we guarantee the existence of stable allocations when all machines are considered public goods, and we start with an initial schedule that might not have the optimal number of machines, but in which agents with large waiting costs are processed first.
    Keywords: Queueing problems, convexity, cost sharing, allocation problems.
    JEL: C44 C71 D61 D63
    Date: 2022
  3. By: Youngsoo Kim; H. Dharma Kwon
    Abstract: In the game of investment in the common good, the free rider problem can delay the stakeholders' actions in the form of a mixed strategy equilibrium. However, it has been recently shown that the mixed strategy equilibria of the stochastic war of attrition are destabilized by even the slightest degree of asymmetry between the players. Such extreme instability is contrary to the widely accepted notion that a mixed strategy equilibrium is the hallmark of the war of attrition. Motivated by this quandary, we search for a mixed strategy equilibrium in a stochastic game of investment in the common good. Our results show that, despite asymmetry, a mixed strategy equilibrium exists if the model takes into account the repeated investment opportunities. The mixed strategy equilibrium disappears only if the asymmetry is sufficiently high. Since the mixed strategy equilibrium is less efficient than pure strategy equilibria, it behooves policymakers to prevent it by promoting a sufficiently high degree of asymmetry between the stakeholders through, for example, asymmetric subsidy.
    Date: 2022–08
  4. By: Anujit Chakraborty (Department of Economics, University of California Davis)
    Abstract: This paper deploys a novel experiment to compare four theories that explain both selfish and non-selfish cooperation. The four theories capture incomplete information (à la Kreps et al. (1982)) alongside the following four non-selfish motives: caring about others (Altruism), being conscientious about cooperation (Duty), enjoying social-efficiency (Efficiency-Seeking), and reciprocity (Sequential Reciprocity). Our experimental design varies the decline-rate of future rewards, under which these theories make contrasting predictions. We find that Efficiency-Seeking is the other-regarding behavior that fits the experimental data best. A Finite Mixture Model analysis finds that 40-49% of our subjects are selfish, 36-45% are Efficiency-seeking, 1-4% are Duty players, and 6-20% are Altruistic.
    JEL: C72 C73 C92
    Date: 2022–09–15
  5. By: José María Alonso-Meijide (Universidade de Santiago de Compostela); Mikel à lvarez-Mozos (Universitat de Barcelona and BEAT); Maria Gloria Fiestras-Janeiro (Universidade de Vigo); Andres Jiménez-Losada (Universidad de Sevilla)
    Abstract: We propose new point valued solutions for global games. We explore the implications of weakening some of the properties used by Gilboa and Lehrer (1991) in their characterization result. Our main contributions are the axiomatic characterizations of two families of values for global games.
    Keywords: Global games, Shapley value, Partition function, Contribution, Lattice.
    JEL: C71
    Date: 2022
  6. By: Ioan Alexandru Puiu; Raphael Andreas Hauser
    Abstract: Spot electricity markets are considered under a Game-Theoretic framework, where risk averse players submit orders to the market clearing mechanism to maximise their own utility. Consistent with the current practice in Europe, the market clearing mechanism is modelled as a Social Welfare Maximisation problem, with zonal pricing, and we consider inflexible demand, physical constraints of the electricity grid, and capacity-constrained producers. A novel type of non-parametric risk aversion based on a defined worst case scenario is introduced, and this reduces the dimensionality of the strategy variables and ensures boundedness of prices. By leveraging these properties we devise Jacobi and Gauss-Seidel iterative schemes for computation of approximate global Nash Equilibria, which are in contrast to derivative based local equilibria. Our methodology is applied to the real world data of Central Western European (CWE) Spot Market during the 2019-2020 period, and offers a good representation of the historical time series of prices. By also solving for the assumption of truthful bidding, we devise a simple method based on hypothesis testing to infer if and when producers are bidding strategically (instead of truthfully), and we find evidence suggesting that strategic bidding may be fairly pronounced in the CWE region.
    Date: 2022–08
  7. By: Wolfram Barfuss; Janusz Meylahn
    Abstract: In this work, we ask for and answer what makes classical reinforcement learning cooperative. Cooperating in social dilemma situations is vital for animals, humans, and machines. While evolutionary theory revealed a range of mechanisms promoting cooperation, the conditions under which agents learn to cooperate are contested. Here, we demonstrate which and how individual elements of the multi-agent learning setting lead to cooperation. Specifically, we consider the widely used temporal-difference reinforcement learning algorithm with epsilon-greedy exploration in the classic environment of an iterated Prisoner's dilemma with one-period memory. Each of the two learning agents learns a strategy that conditions the following action choices on both agents' action choices of the last round. We find that next to a high caring for future rewards, a low exploration rate, and a small learning rate, it is primarily intrinsic stochastic fluctuations of the reinforcement learning process which double the final rate of cooperation to up to 80\%. Thus, inherent noise is not a necessary evil of the iterative learning process. It is a critical asset for the learning of cooperation. However, we also point out the trade-off between a high likelihood of cooperative behavior and achieving this in a reasonable amount of time. Our findings are relevant for purposefully designing cooperative algorithms and regulating undesired collusive effects.
    Date: 2022–09
  8. By: Bernard Caillaud (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Ariane Lambert-Mogiliansky (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: In this paper we investigate the Investor-State Dispute Resolution Settlement (ISDS) framework, which governs dispute resolution between foreign investors and host states in many bilateral and multilateral trade agreements. We show that ISDS delivers fair justice in a one-shot setting. In a repeated-interaction setting however, it is prone to collusion to the benefit of all parties except the host states. Three factors are determinant: First, the investors are the sole parties able to file cases; Second, arbitrators' earning prospects depend on the investors' filing cases; And finally, treaties leave substantial discretion to arbitration courts in their interpretation of treaties' provisions. We give conditions for pro-business collusion between investors and arbitrators to develop and we show how it makes it profitable for foreign investors to file high-stake claims against states in response to new environmental, social or health regulations. Further, we address regulatory chill and show how the fear of ISDS attacks can hold back welfare improving regulation in the host country. Finally, we extend the model to show how regulatory chill affect policy-making in other countries in which the investor operates with similar activities.
    Date: 2022–08
  9. By: William Brock; Bo Chen; Steven N. Durlauf; Shlomo Weber
    Abstract: Immigrants in economies with a dominant native language exhibit substantial heterogeneities in language acquisition of the majority language. We model partial equilibrium language acquisition as an equilibrium phenomenon. We consider an environment where heterogeneous agents from various minority groups choose whether to acquire a majority language fully, partially, or not at all. Different acquisition decisions confer different communicative benefits and incur different costs. We offer an equilibrium characterization of language acquisition strategies and find that partial acquisition can arise as an equilibrium behavior. We also show that a language equilibrium may exhibit insufficient learning relative to the social optimum. In addition, we provide a local stability analysis of steady state language equilibria. Finally, we discuss econometric implementation of the language acquisition model and establish identification conditions.
    JEL: C72 D61 J15 Z13
    Date: 2022–08
  10. By: Broccardo, Eleonora; Hart, Oliver D.; Zingales, Luigi
    Abstract: We study the relative effectiveness of exit (divestment and boycott) and voice (engagement) strategies in promoting socially desirable outcomes in companies that generate externalities. We show that if the majority of investors are socially responsible, voice achieves the socially desirable outcome, while exit does not. If the majority of investors are purely selfish, exit is a more effective strategy, but neither strategy generally achieves the first best. We also show that individual incentives to join an exit strategy are not aligned with social incentives, and hence exit can lead to a worse outcome than if all individuals are purely selfish.
    Keywords: Exit,Voice,Social Responsibility,Divestment,Boycott,Engagement
    JEL: D02 D21 D23 D62 D64 H41 L21
    Date: 2021
  11. By: Meena Jagadeesan; Michael I. Jordan; Nika Haghtalab
    Abstract: Competition between traditional platforms is known to improve user utility by aligning the platform's actions with user preferences. But to what extent is alignment exhibited in data-driven marketplaces? To study this question from a theoretical perspective, we introduce a duopoly market where platform actions are bandit algorithms and the two platforms compete for user participation. A salient feature of this market is that the quality of recommendations depends on both the bandit algorithm and the amount of data provided by interactions from users. This interdependency between the algorithm performance and the actions of users complicates the structure of market equilibria and their quality in terms of user utility. Our main finding is that competition in this market does not perfectly align market outcomes with user utility. Interestingly, market outcomes exhibit misalignment not only when the platforms have separate data repositories, but also when the platforms have a shared data repository. Nonetheless, the data sharing assumptions impact what mechanism drives misalignment and also affect the specific form of misalignment (e.g. the quality of the best-case and worst-case market outcomes). More broadly, our work illustrates that competition in digital marketplaces has subtle consequences for user utility that merit further investigation.
    Date: 2022–08
  12. By: Bergeot, J.;
    Abstract: Do children cooperate when they decide to provide informal care to their elderly parent? This paper assesses which model drives the caregiving decisions of children. I compare the pre-dictive power of two models: a (joint-utility) cooperative and a Nash noncooperative model. I focus on families with two children and one single parent. e model allows caregiving by one child to have a direct externality on the well-being of the sibling. The results suggest that the cooperative model overestimates the level of care received by the parents observed in the data and its predictive power is outperformed by the noncooperative model. is suggests that children are more likely to behave according to a noncooperative model. I also find that children’s participation in caregiving has a positive externality on the well-being of the sibling. I construct an indicator of the degree of noncooperativeness between children and show that it is positively correlated with the number of unmet needs the parent has. I conclude that, because children do not internalize the positive externality when they behave noncooperatively, the current level of informal care provided to parents appears to suffer from a public good problem.
    Date: 2022–07
  13. By: Ville Korpela (Turku School of Economics, University of Turku); Michele Lombardi (University of Liverpool Management School, Liverpool, UK and Department of Economics and Statistics, University of Napoli Federico II); Riccardo D. Saulle (Department of Economics and Management, University of Padova)
    Abstract: We fully identify the class of social choice functions that are implementable in von Neumann Morgenstern (vNM) stable set (von Neumann and Morgenstern, 1944) by a rights structure. A rights structure formalizes the idea of power distribution in a society. Following Harsanyi’critique (Harsanyi, 1974), we also study implementation problems in vNM stable set that are robust to farsighted reasoning.
    Keywords: stable set, implementation, rights structure, farsightedness
    JEL: C71 D02 D71 D82
    Date: 2022–09
  14. By: Pierre C. Boyer (CREST, Ecole Polytechnique, Institut Polytechnique de Paris); Christoph Esslinger (Managing Director; Brian Roberson (Purdue University, Department of Economics, Krannert School of Management)
    Abstract: How do electoral incentives influence the choice to experiment with a policy that generates uncertain future benefits? To answer this question, we examine a two-period model of redistributive politics with uncertain policy outcomes involving a mixture of private and public benefits. In equilibrium, we find that the intertemporal tradeoff between current policy costs and future benefits creates an incentive for politicians to use public debt to smooth spending across periods. The higher the share of policy that are in the form of a public good, the higher the level of available debtrelated spending on targeted policies that is necessary.
    Keywords: Political Competition; Public Debt; Reforms; Redistributive Politics; Debt and Spending Limits.
    JEL: C72 D72 D78 H6
    Date: 2022–08–15

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