nep-gth New Economics Papers
on Game Theory
Issue of 2022‒07‒18
seventeen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Credible equilibrium By Mehmet S. Ismail
  2. Discrimination in Heterogeneous Games By Annick Laruelle; Andr\'e Rocha
  3. Sado-Masochism in Buchanan's Samaritan's Dilemma. A Constitutional Perspective By Alain Marciano
  4. The art of brevity By Alonso, Ricardo; Rantakari, Heikki
  5. Leveraging the Honor Code: Public Goods Contributions under Oath By Jérôme Hergueux; Nicolas Jacquemet; Stéphane Luchini; Jason Shogren
  6. On the optimal management of environmental stock externalities By Anastasios Xepapadeas
  7. Continuous versus Discrete Time in Dynamic Common Pool Resource Game Experiments By Anmina Murielle Djiguemde; Dimitri Dubois; Alexandre Sauquet; Mabel Tidball
  8. Strategy Assortativity and the Evolution of Parochialism By Ennio Bilancini; Leonardo Boncinelli; Alessandro Tampieri
  9. Strategic Real Option Exercising and Second-mover Advantage By Min Dai; Zhaoli Jiang; Neng Wang
  10. Entry in first-price auctions with signaling By Bos, Olivier; Truyts, Tom
  11. Key players in bullying networks By Ata Atay; Ana Mauleon; Simon Schopohl; Vincent Vannetelbosch
  12. Variable importance without impossible data By Masayoshi Mase; Art B. Owen; Benjamin B. Seiler
  13. Concord and contention in a dynamic bargaining experiment with costly conflict By Lian Xue; Stefania Sitzia; Theodore L. Turocy
  14. A Game-Theory Analysis of Electric Vehicle Adoption in Beijing under License Plate Control Policy By Lijing Zhu; Jingzhou Wang; Arash Farnoosh; Xunzhang Pan
  15. The Strategic Jump - The Order Effect on Winning “The Final Three” in Long Jump Competitions By Karlsson, Niklas; Lunander, Anders
  16. On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces By Robert M. Anderson; Haosui Duanmu; Aniruddha Ghosh; M. Ali Khan
  17. State-dependent Central Bank Communication with Heterogeneous Beliefs By Herbert Sylvérie

  1. By: Mehmet S. Ismail
    Abstract: Credible equilibrium is a solution concept that imposes a stronger credibility notion than subgame perfect equilibrium. A credible equilibrium is a refinement of subgame perfect equilibrium such that if a threat in a subgame g is "credible," then it must also be credible in every subgame g' that is "equivalent" to g. I show that (i) a credible equilibrium exists in multi-stage games, and (ii) if every stage game has a unique Nash equilibrium, then the credible equilibrium is unique even in infinite horizon multi-stage games. Moreover, in perfect information games, credible equilibrium is equivalent to subgame perfect equilibrium.
    Date: 2022–06
  2. By: Annick Laruelle; Andr\'e Rocha
    Abstract: In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show that there exists symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Moreover, discrimination has a limit: the maximum number of groups where the treatment differs is three. We then discuss the theoretical results in light of the observed behavior of people in some specific psychological contexts.
    Date: 2022–06
  3. By: Alain Marciano (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier, UM - Université de Montpellier)
    Abstract: In this paper, we study the impact of altruism on an interaction between a samaritan and a recipient/parasite in the frame of Buchanan's samaritan's dilemma (1975). We show that, as soon as altruism reaches a certain threshold, the equilibrium of the game corresponds to the situation Buchanan called a samaritan's dilemma. We also show that the Nash equilibrium reached for these levels of altruism is a Pareto-efficient outcome. Thus, the situation Buchanan characterized as a samaritan's dilemma is not a dilemma at all. Both players are satisfied with the situation as it is and need each other, up to the point of giving birth to a sado-masochistic equilibrium. We also show that this result holds if and only if the constitutional rules are given-either the ethical rules followed by the individuals, or the form of the game. This equilibrium could be avoided if the players adopted a constitutional perspective on the situation.
    Keywords: Masochism,Altruism,Samaritan's dilemma,Buchanan,Exploitation,Sadism
    Date: 2022
  4. By: Alonso, Ricardo; Rantakari, Heikki
    Abstract: We analyze a class of sender-receiver games with quadratic payoffs, which includes the communication games in Alonso et al. (2008) and Rantakari (2008) as special cases, for which the sender's or the receiver's maximum expected payoff when players have access to arbitrary, mediated communication protocols is attained in one round of face-to-face, unmediated cheap talk. This result is based on the existence for these games of a communication equilibrium with an infinite number of partitions of the state space. We provide explicit expressions for the maximum expected payoff of the sender and the receiver, and illustrate its use by deriving new comparative statics of the quality of optimal communication. For instance, a shift in the underlying uncertainty that reduces expected conflict can worsen the quality of communication.
    Keywords: communication equilibrium; information transmission; mediation; one-shot cheap talk; Elsevier deal
    JEL: C72 D70 D83
    Date: 2022–03–01
  5. By: Jérôme Hergueux (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Nicolas Jacquemet (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Stéphane Luchini (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Jason Shogren (UW - University of Wyoming)
    Abstract: Public good games are at the core of many environmental challenges. In such social dilemmas, a large share of people endorse the norm of reciprocity. A growing literature complements this finding with the observation that many players exhibit a self-serving bias in reciprocation: "weak reciprocators" increase their contributions as a function of the effort level of the other players, but less than proportionally. In this paper, we build upon a growing literature on truth-telling to argue that weak reciprocity might be best conceived not as a preference, but rather as a symptom of an internal trade-off at the player level between (i) the truthful revelation of their private reciprocal preference, and (ii) the economic incentives they face (which foster free-riding). In truth-telling experiments, many players misrepresent private information when this is to their material benefit, but to a significantly lesser extent than what would be expected based on the profit-maximizing strategy. We apply this behavioral insight to strategic situations, and test whether the preference revelation properties of the classic voluntary contribution game can be improved by offering players the possibility to sign a classic truth-telling oath. Our results suggest that the honesty oath helps increase cooperation (by 33% in our experiment). Subjects under oath contribute in a way which is more consistent with (i) the contribution they expect from the other players and (ii) their normative views about the right contribution level. As a result, the distribution of social types elicited under oath differs from the one observed in the baseline: some free-riders, and many weak reciprocators, now behave as pure reciprocators.
    Keywords: Cooperation,Reciprocity,Social preferences,Public goods,Truth-telling oath
    Date: 2022–03
  6. By: Anastasios Xepapadeas
    Abstract: Following a brief review of the management of environmental externalities under strategic interactions in the traditional temporal domain, results are extended to the spatiotemporal domain. Conditions for spatial open-loop and feedback Nash equilibria, along with conditions for the benchmark cooperative solution, are presented and compared. A simplified numerical example illustrates the spatial patterns emerging at a steady state under Fickian diffusion and dispersal kernels, and the inefficiency of spatially-flat emission taxes. This conceptual framework could provide new research areas.
    Keywords: spatial diffusion, dispersion kernel, open-loop Nash equilibrium, feedback Nash equilibrium, cooperative solution, steady state, optimal emission tax
    Date: 2022–04–20
  7. By: Anmina Murielle Djiguemde (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro - Montpellier SupAgro - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Dimitri Dubois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro - Montpellier SupAgro - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Alexandre Sauquet (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro - Montpellier SupAgro - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro - Montpellier SupAgro - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)
    Abstract: We study the impact of discrete versus continuous time on the behavior of agents in the context of a dynamic common pool resource game. To this purpose, we consider a linear quadratic model and conduct a lab experiment in which agents exploit a renewable resource with an infinite horizon. We use a differential game for continuous time and derive its discrete time approximation. In the single agent setting, we fail to detect, on a battery of indicators, any difference between agents' behavior in discrete and continuous time. Conversely, in the two-player setting, significantly more agents can be classified as myopic and end up with a low resource level in discrete time. Continuous time seems to allow for better cooperation and thus greater sustainability of the resource than does discrete time.
    Keywords: Common Pool Resource,Differential Games,Experimental Economics,Continuous Time,Discrete Time
    Date: 2022
  8. By: Ennio Bilancini; Leonardo Boncinelli; Alessandro Tampieri
    Abstract: This paper investigates the role of strategy assortativity for the evolution of parochialism. Individuals belonging to different groups are matched in pairs to play a prisoner’s dilemma, conditioning their choice on the identity of the partner. Strategy assortativity implies that a player is more likely to be matched with someone playing the same strategy. We find that, if the degree of strategy assortativity is sufficiently high, then parochialism (i.e., cooperate with your own group and defect with others) spreads over a group, while egoism (i.e., defect with everyone) emerges otherwise. Notably, parochialism is more likely to emerge in smaller groups.
    Keywords: prisoner's dilemma, cooperation, in-group favoritism, cultures, asymptotic stability
    JEL: C72 C73 Z10
    Date: 2022
  9. By: Min Dai; Zhaoli Jiang; Neng Wang
    Abstract: Many real-world business opportunities feature second-mover advantages as there are often positive spillovers (externality) from early entrants to followers. We develop a tractable stochastic duopoly entry game with a second-mover advantage. We show that firms engage in a war-of-attrition game with the hope of becoming the follower, resulting in excessively delayed entry opposite to the predictions that competition causes firms to equalize rents (Fudenberg and Tirole, 1985) by exercising their entry options too soon (Grenadier, 1996). We obtain closed-form value functions and entry strategies for both mixed-strategy and pure-strategy equilibria. We develop a separation principle that decomposes the duopoly real-option game into a monopolist's real-option problem and a generalized easy-to-solve war-of-attrition game with stochastic payoffs. Quantitatively, our model predicts substantial option value erosion caused by excessively delayed firm entry.
    JEL: E22 G13 G31
    Date: 2022–06
  10. By: Bos, Olivier; Truyts, Tom
    Abstract: We study the optimal entry fee in a symmetric private value first-price auction with signaling, in which the participation decisions and the auction outcome are used by an outside observer to infer the bidders' types. We show that this auction has a unique fully separating equilibrium bidding function. When the bidders' sensibility for the signaling concern is sufficiently strong, the expected revenue maximizing entry fee is the maximal fee that guarantees full participation. The larger is the bidder's sensibility, the higher is the optimal participation.
    Keywords: first-price auction,entry,monotonic signaling,social status
    JEL: D44 D82
    Date: 2022
  11. By: Ata Atay (Universitat de Barcelona and BEAT); Ana Mauleon (CEREC, UCLouvain Saint-Louis Brussels and CORE/LIDAM, UCLouvain, Belgium); Simon Schopohl (CEREC, UCLouvain Saint-Louis Brussels, Belgium); Vincent Vannetelbosch (CORE/LIDAM, UCLouvain, Belgium)
    Abstract: Individuals are embedded in a network of relationships and they can be victims, bystanders, or perpetrators of bullying and harassment. Each individual decides noncooperatively how much effort to exert in preventing misbehavior. Each individual's optimal effort depends on the contextual effect, the social multiplier effect and the social conformity effect. We characterize the Nash equilibrium and we derive an inter-centrality measure for finding the key player who once isolated increases the most the aggregate effort. An individual is more likely to be the key player if she is influencing many other individuals, she is exerting a low effort because of her characteristics, and her neighbors are strongly influenced by her. The key player policy increases substantially the aggregate effort and the targeted player should never be selected randomly. The key player is likely to remain the key player in presence of social workers except if she is becoming much less influential due to her closeness to social workers. Finally, we consider alternative policies (e.g. training bystanders for helping victims) and compare them to the policy of isolating the key player.
    Keywords: Social networks, bullying, harassment, peer effects, key player, conformity,
    JEL: A14 C72 D85 Z13
    Date: 2022
  12. By: Masayoshi Mase; Art B. Owen; Benjamin B. Seiler
    Abstract: The most popular methods for measuring importance of the variables in a black box prediction algorithm make use of synthetic inputs that combine predictor variables from multiple subjects. These inputs can be unlikely, physically impossible, or even logically impossible. As a result, the predictions for such cases can be based on data very unlike any the black box was trained on. We think that users cannot trust an explanation of the decision of a prediction algorithm when the explanation uses such values. Instead we advocate a method called Cohort Shapley that is grounded in economic game theory and unlike most other game theoretic methods, it uses only actually observed data to quantify variable importance. Cohort Shapley works by narrowing the cohort of subjects judged to be similar to a target subject on one or more features. A feature is important if using it to narrow the cohort makes a large difference to the cohort mean. We illustrate it on an algorithmic fairness problem where it is essential to attribute importance to protected variables that the model was not trained on. For every subject and every predictor variable, we can compute the importance of that predictor to the subject's predicted response or to their actual response. These values can be aggregated, for example over all Black subjects, and we propose a Bayesian bootstrap to quantify uncertainty in both individual and aggregate Shapley values.
    Date: 2022–05
  13. By: Lian Xue (Wuhan University); Stefania Sitzia (University of East Anglia); Theodore L. Turocy (University of East Anglia)
    Abstract: We report experimental results from a dynamic real-time bargaining experiment. Players earn flows of income from the assets they control at any point in the bargaining process (concord), while they incur costs which are proportional to the size of the conflict between players current claims (contention). We find that most bargaining interactions are characterised by small but non-zero amounts of contention, which arises from the process of tacitly coordinating claims, including from negotiating turn-taking approaches. Interactions with large losses from contention occur in a sizeable minority of interactions. We find differences across participants in how much contention they engage in, and the number of assets they hold.
    Keywords: Bargaining; continuous time; turn-taking; locus of control; experiment.
    JEL: C72 C91 C92
    Date: 2022–06
  14. By: Lijing Zhu (China University of Petroleum); Jingzhou Wang (China University of Petroleum, IFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvelles, IFP School); Arash Farnoosh (IFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvelles, IFP School); Xunzhang Pan (China University of Petroleum)
    Abstract: To reduce traffic congestion and protect the environment, license plate control (LPC) policy has been implemented in Beijing since 2011. In 2019, 100,000 vehicle license plates were distributed, including 60,000 for electric vehicles (EVs) and 40,000 for gasoline vehicle (GVs). However, whether the current license plate allocation is optimal from a social welfare maximization perspective remains unclear. This paper proposes a two-level Stackelberg game, which portrays the interaction between vehicle applicants and the government to quantify the optimal number of EV license plates under the LPC policy in Beijing. The equilibrium number of EV license plates derived from the Stackelberg model is 58,800, which could increase the social welfare by 0.38%. Sensitivity analysis is conducted to illustrate the impact of important influential factors — total license plate quota, vehicle rental fee, and energy price — on EV adoption. The LPC policy under COVID-19 is also studied through a scenario analysis. If the government additionally increases the total quota by 20,000, 24% could be allocated to GV and 76% to EV. One third reduction of the current vehicle rental fee could increase EV license plates by 10.5%. In terms of energy prices, when gasoline price is low, reducing electricity prices could contribute to EV adoption significantly, while that effect tapers off as gasoline prices increase.
    Keywords: Electric vehicle,License plate control (LPC) policy,Stackelberg game theory,License plate quota
    Date: 2022–04
  15. By: Karlsson, Niklas (Örebro University School of Business); Lunander, Anders (Örebro University School of Business)
    Abstract: The tournament rules for long jump competitions have changed in recent years. Today, only the three athletes with the best jumps from the five initial attempts are qualified to make an additional sixth jump – a format called The Final Three. In the first implemented version of The Final Three, the top athletes sequentially make one final jump, starting with the athlete ranked third place from the initial attempts. The athlete with the longest jump in this sixth attempt wins the competition, irrespective of achieved results in previous attempts. In this study, we analyze the effect of the athletes’ jump order on the probability of winning the competition within this first implemented version of The Final Three. We derive the final’s symmetric subgame perfect equilibrium and compute the corresponding equilibrium winning probabilities, given the values assigned to the distributional parameters. The modelling of the game is preceded by a development of a stochastic model for the outcome in long jumping. An athlete affects the distribution of the outcome by choosing where to start her approach run. Our results indicate a last mover advantage, albeit small. The athlete jumping last, wins the final with a probability 0.35, followed by the athlete jumping second with a probability 0.33 to win the final.
    Keywords: OR in sports; sequential game; order effect
    JEL: C49 C72 D81 Z20
    Date: 2022–04–01
  16. By: Robert M. Anderson; Haosui Duanmu; Aniruddha Ghosh; M. Ali Khan
    Abstract: We present theorems on the existence of Berk-Nash equilibria in misspecified Markov Decision Processes with infinite action and state spaces. We extend the results of Esponda-Pouzo (2021) for finite state and action spaces to compact action spaces and sigma-compact state spaces with possibly unbounded payoff functions. This extension allows, for the first time, consideration of continuous distributions with possibly unbounded support. We provide several examples that span various areas in economic theory: neo-classical producer theory, the optimal savings problem, and identification and inference in econometric theory. The proofs use a recent technique in nonstandard analysis, originated by the second author, to extend known theorems for finite mathematical systems to infinite systems. This technique has already generated new results in probability theory, statistical decision theory, and general equilibrium theory, and is potentially applicable to a wide range of problems.
    Date: 2022–06
  17. By: Herbert Sylvérie
    Abstract: This paper studies how state-contingent central bank communication can improve welfare when externalities are at play. In the model, a central banker (CB) wants to influence the private sector beliefs, which are heterogeneous, to generate an upward bias in their action. The CB can engender such welfare-improving bias by providing public information, choosing a signalling strategy that is a function of fundamentals. To study this optimal communication strategy, I introduce heterogeneous priors in an otherwise standard Bayesian persuasion model à la Gentzkow and Kamenica (2011) and characterize the dependence of optimal disclosure on the heterogeneity of beliefs. I show that heterogeneity matters in two ways: (i) it is optimal to send moderating signals, which implies sending signals with positive error probabilities in both states, and constitutes a non-trivial departure from the homogeneous beliefs case; (ii) higher dispersion in beliefs leads the monetary authority to send signals with lower error probabilities. I apply my framework to a central bank communication problem in which the policy maker communicates about aggregate conditions to influence firms' investment decisions in presence of investment externalities. I empirically validate the model's predictions by showing that the FOMC unemployment rate forecasts are systematically biased in opposite directions in recessions and expansions. Also in line with the model's predictions, the forecast biases are decreasing in the degree of private sector disagreement for each state.
    Keywords: Central Bank Communication, Bayesian Persuasion, Expectations, Forecasts
    JEL: E52 E58 D83
    Date: 2022

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