nep-gth New Economics Papers
on Game Theory
Issue of 2021‒05‒24
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Strategic information transmission with sender’sapproval By Renault, Jérôme; Forges, Françoise
  2. Anger and Strategic Behavior: A Level-k Analysis By Castagnetti, Alessandro; Proto, Eugenio
  3. Strategic Ambiguity in Global Games By Takashi Ui
  4. Stationary Discounted and Ergodic Mean Field Games of Singular Control By Haoyang Cao; Jodi Dianetti; Giorgio Ferrari
  5. Continuous versus Discrete Time in Dynamic Common Pool Resource Game Experiments By Anmina Murielle Djiguemde; Dimitri Dubois; Alexandre Sauquet; Tidball Mabel
  6. Repeated Games with Switching Costs: Stationary vs History-Independent Strategies By Yevgeny Tsodikovich; Xavier Venel; Anna Zseleva
  7. Non-convergence to stability in coalition formation games By Agustín G. Bonifacio; Elena Inarra; Pablo Neme
  8. Binary Outcomes and Linear Interactions By Boucher, Vincent; Bramoullé, Yann
  9. Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections By Evan Piermont; Peio Zuazo-Garin
  10. Agenda-Setter Power Dynamics: Learning in Multi-Issue Bargaining By Bowen, T. Renee; Hwang, Ilwoo; Krasa, Stefan
  11. Calibrated Click-Through Auctions: An Information Design Approach By Dirk Bergemann; Paul Duetting; Renato Paes Leme; Song Zuo
  12. Cohort Shapley value for algorithmic fairness By Masayoshi Mase; Art B. Owen; Benjamin B. Seiler
  13. Collective Information Acquisition By Eilat, Ran; Eliaz, Kfir
  14. Trends in the E-commerce and in the Traditional Retail Sectors During the Covid-19 Pandemic: an Evolutionary Game Approach By Andr\'e Barreira da Silva Rocha; Matheus Oliveira Meirim; Lara Corr\^ea Nogueira
  15. Efficiency and stability in the connections model with heterogeneous node By Olaizola, Norma; Valenciano, Federico
  16. Government Intervention through Informed Trading in Financial Markets By Huang, Shao'an; Qiu, Zhigang; Wang, Gaowang; Wang, Xiaodan
  17. Let's Collude By Aghadadashli, Hamid; Legros, Patrick
  18. Compositionality in Game Theory: an Operadic View By Fernando Tohmé
  19. Nonlinear Pricing in Oligopoly: How Brand Preferences Shape Market Outcomes By Gomes, Renato; Lozachmeur, Jean-Marie; Maestri, Lucas
  20. Direct-to-Consumer sales by manufacturers and bargaining. By Javier Donna; Pedro Pereira; Andre Trindade; Renan Yoshida
  21. The Best at the Top? Candidate Ranking Strategies Under Closed List Proportional Representation By Benoit S Y Crutzen; Hideo Konishi; Nicolas Sahuguet

  1. By: Renault, Jérôme; Forges, Françoise
    Abstract: We consider a sender-receiver game with an outside option for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject. We study situations in which the sender’s approval is crucial to the receiver. We show that a partitional, (perfect Bayesian Nash) equilibrium exists if the sender has only two types or if the receiver’s preferences over decisions do not depend on the type of the sender as long as the latter participates. The result does not extend: we construct a counter-example (with three types for the sender and type-dependent affine utility functions) in which there is no mixed equilibrium. In the three type case, we provide a full characterization of (possibly mediated) equilibria.
    JEL: C7 C72 C78 C
    Date: 2021–05
  2. By: Castagnetti, Alessandro; Proto, Eugenio
    Abstract: Anger is an important driver in shaping economic activities, particularly in instances that involve strategic interactions between individuals. Here we test whether anger impairs the capacity to think strategically, and we analyze the implications of our result on bargaining and cooperation games. Accordingly, with a preregistered experiment (Experiment 1), we externally induce anger to a subgroup of subjects following a standard procedure that we verify by using a novel method of text analysis. We show that anger can impair the capacity to think strategically in a beauty contest game. Angry subjects choose numbers further away from the Nash equilibrium, and earn significantly lower profits. A structural analysis estimates that there is an increase in the share of level-zero players in the treated group compared to the control group. Furthermore, with a second preregistered experiment (Experiment 2), we show that this effect is not common to all negative emotions. Sad subjects do not play significantly further away from the Nash equilibrium than the control group in the same beauty contest game of Experiment 1, and sadness does not lead to more level-zero play.
    Keywords: anger; beauty-contest; induced emotions; Strategic Interactions
    JEL: C92 D90 D91
    Date: 2020–09
  3. By: Takashi Ui (Hitotsubashi University)
    Abstract: In incomplete information games with ambiguous information, rational behavior depends on fundamental ambiguity (ambiguity about states) and strategic ambiguity (ambiguity about others’ actions). We study the impact of strategic ambiguity in global games, which is evident when one of the actions yields a constant payoff. Ambiguous-quality information makes more players choose this action, whereas (unambiguous) low-quality information makes more players choose an ex-ante best response to the uniform belief over the opponents’ actions. If the ex-ante best-response action yields a constant payoff, sufficiently ambiguous-quality information makes most players choose this action, thus inducing a unique equilibrium, whereas sufficiently low-quality information generates multiple equilibria. In applications to financial crises, we demonstrate that news of more ambiguous quality triggers a debt rollover crisis, whereas news of less ambiguous quality triggers a currency crisis.
    JEL: C72 D81 D82
    Date: 2021–03
  4. By: Haoyang Cao; Jodi Dianetti; Giorgio Ferrari
    Abstract: We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean field equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean field equilibria for the discounted and the ergodic games by showing the validity of an Abelian limit. The latter allows also to approximate Nash equilibria of - so far unexplored - symmetric N-player ergodic singular control games through the mean field equilibrium of the discounted game. Numerical examples finally illustrate in a case study the dependency of the mean field equilibria with respect to the parameters of the games.
    Date: 2021–05
  5. By: Anmina Murielle Djiguemde (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Dimitri Dubois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Alexandre Sauquet (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Tidball Mabel (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche 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 in which agents exploit a renewable resource with an infinite horizon and conduct a lab experiment. We use a differential game for continuous time and derive its discrete time approximation. When the agent is the sole owner of the resource, we fail to detect on a battery of indicators any difference between 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. Also, payoffs are more equally distributed in the continuous time setting.
    Keywords: Common Pool Resource,Differential Games,Experimental Economics,Continuous Time,Discrete Time
    Date: 2021–05–03
  6. By: Yevgeny Tsodikovich (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); Xavier Venel (Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]); Anna Zseleva (Department of Quantitative Economics, School of Business and Economics, Maastricht University)
    Abstract: We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.
    Keywords: Switching Costs,Repeated Games,Stochastic Games,Zero-sum games
    Date: 2021–05–10
  7. By: Agustín G. Bonifacio (Universidad Nacional de San Luis/CONICET); Elena Inarra (University of the Basque Country); Pablo Neme (Universidad Nacional de San Luis/CONICET)
    Abstract: We study the problem of convergence to stability in coalition formation games in which the strategies of each agent are coalitions in which she/he can partici- pate and outcomes are coalition structures. Given a natural blocking dynamic, an absorbing set is a minimum set of coalition structures that once reached is never abandoned. The coexistence of single and non-single absorbing sets is what causes lack of convergence to stability. To characterize games in which both types of set are present, we first relate circularity among coalitions in preferences (rings) with circularity among coalition structures (cycles) and show that there is a ring in pref- erences if and only if there is a cycle in coalition structures. Then we identify a special configuration of overlapping rings in preferences characterizing games that lack convergence to stability. Finally, we apply our findings to the study of games induced by sharing rules.
    Keywords: Coalition formation Matching markets Absorbing sets Convergence to stability
    JEL: C71 C78
    Date: 2020–09
  8. By: Boucher, Vincent; Bramoullé, Yann
    Abstract: Heckman and MaCurdy (1985) first showed that binary outcomes are compatible with linear econometric models of interactions. This key insight was unduly discarded by the literature on the econometrics of games. We consider general models of linear interactions in binary outcomes that nest linear models of peer effects in networks and linear models of entry games. We characterize when these models are well defined. Errors must have a specific discrete structure. We then analyze the models' game-theoretic microfoundations. Under complete information and linear utilities, we characterize the preference shocks under which the linear model of interactions forms a Nash equilibrium of the game. Under incomplete information and independence, we show that the linear model of interactions forms a Bayes-Nash equilibrium if and only if preference shocks are iid and uniformly distributed. We also obtain conditions for uniqueness. Finally, we propose two simple consistent estimators. We revisit the empirical analyses of teenage smoking and peer effects of Lee, Li, and Lin (2014) and of entry into airline markets of Ciliberto and Tamer (2009). Our reanalyses showcase the main interests of the linear framework and suggest that the estimations in these two studies suffer from endogeneity problems.
    Keywords: Binary Outcomes; Econometrics of Games; Linear Probability Model; peer effects
    Date: 2020–11
  9. By: Evan Piermont; Peio Zuazo-Garin
    Abstract: In dynamic settings each economic agent's choices can be revealing of her private information. This elicitation via the rationalization of observable behavior depends each agent's perception of which payoff-relevant contingencies other agents persistently deem as impossible. We formalize the potential heterogeneity of these perceptions as disagreements at higher-orders about the set of payoff states of a dynamic game. We find that apparently negligible disagreements greatly affect how agents interpret information and assess the optimality of subsequent behavior: When knowledge of the state space is only 'almost common', strategic uncertainty may be greater when choices are rationalized than when they are not--forward and backward induction predictions, respectively, and while backward induction predictions are robust to small disagreements about the state space, forward induction predictions are not. We also prove that forward induction predictions always admit unique selections a la Weinstein and Yildiz (2007) (also for spaces not satisfying richness) and backward induction predictions do not.
    Date: 2021–05
  10. By: Bowen, T. Renee; Hwang, Ilwoo; Krasa, Stefan
    Abstract: We study a dynamic bargaining model between a fixed agenda-setter and responder over successive issues. If the responder rejects the setter's proposal, the setter can attempt to assert her will to implement her ideal and will succeed with a probability that depends on her "personal power". The players learn about the setter's power as gridlock persists. Gridlock occurs when the setter's perceived power is either too high or too low, and the players reach compromise in an intermediate interval of beliefs. The presence of "difficult" issues can induce more compromise as the players have incentives to avoid learning.
    Keywords: Bargaining; Gridlock; learning; Power
    JEL: C78 D72 D74 D83
    Date: 2020–10
  11. By: Dirk Bergemann (Cowles Foundation, Yale University); Paul Duetting (Google Research); Renato Paes Leme (Google Research); Song Zuo (Google Research)
    Abstract: We analyze the optimal information design in a click-through auction with ï¬ xed valuations per click, but stochastic click-through rates. While the auctioneer takes as given the auction rule of the click-through auction, namely the generalized second-price auction, the auctioneer can design the information flow regarding the click-through rates among the bidders. A natural requirement in this context is to ask for the information structure to be calibrated in the learning sense. With this constraint, the auction needs to rank the ads by a product of the bid and an unbiased estimator of the click-through rates, and the task of designing an optimal information structure is thus reduced to the task of designing an optimal unbiased estimator. We show that in a symmetric setting with uncertainty about the click-through rates, the optimal information structure attains both social efficiency and surplus extraction. The optimal information structure requires private (rather than public) signals to the bidders. It also requires correlated (rather than independent) signals, even when the underlying uncertainty regarding the click-through rates is independent. Beyond symmetric settings, we show that the optimal information structure requires partial information disclosure.
    Keywords: Click-Through Rates, Information Design, Second-Price Auction, Calibration, Private Signals, Public Signals, Conflation
    JEL: D44 D47 D82
    Date: 2021–05
  12. By: Masayoshi Mase; Art B. Owen; Benjamin B. Seiler
    Abstract: Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known COMPAS recidivism data as our example. This approach allows one to identify for each individual in a data set the extent to which they were adversely or beneficially affected by their value of a protected attribute such as their race. The method can do this even if race was not one of the original predictors and even if it does not have access to a proprietary algorithm that has made the predictions. The grounding in game theory lets us define aggregate variable importance for a data set consistently with its per subject definitions. We can investigate variable importance for multiple quantities of interest in the fairness literature including false positive predictions.
    Date: 2021–05
  13. By: Eilat, Ran; Eliaz, Kfir
    Abstract: We consider the problem faced by a group of players who need to collectively decide what public signal to acquire, and how to share its cost, before voting on whether to take some action, when each player is privately informed about his state-dependent payoffs from the action. We characterize the welfare maximizing mechanism for information acquisition taking into account the subsequent voting game. We identify novel distortions that arise from the information asymmetry and from the fact that after observing the signal realization, the players vote independently of their actions in the mechanism.
    Keywords: collective decision-making; Information-design; Mechanism-Design; Public Good Provision; rational inattention
    Date: 2020–09
  14. By: Andr\'e Barreira da Silva Rocha; Matheus Oliveira Meirim; Lara Corr\^ea Nogueira
    Abstract: An evolutionary game model is developed to study the interplay between consumers and producers when trade takes place on an e-commerce marketplace. The type of delivery service available and consumers' taste are particularly important regarding both game payoffs and players' strategies. The game payoff matrix is then adapted to analyse the different trading patterns that were developed during the COVID-19 pandemic in both the traditional retail and e-commerce sectors. In contrast to the former, investment in logistics and warehouses in the e-commerce sector allowed for the emergence of a trend in which fast delivery and eager consumers are becoming the norm.
    Date: 2021–05
  15. By: Olaizola, Norma; Valenciano, Federico
    Abstract: This paper studies the connections model (Jackson and Wolinsky, 1996) when nodes may have different values. It is shown that efficiency is reached by a strongly hierarchical structure that we call strong NSG-networks: Nested Split Graph networks where the hierarchy or ranking of nodes inherent in any such network is consistent with the rank of nodes according to their value, perhaps leaving some of the nodes with the lowest values disconnected. A simple algorithm is provided for calculating these efficient networks. We also introduce a natural extension of pairwise stability assuming that players are allowed to agree on how the cost of each link is split and prove that stability in this sense for connected strong NSG-networks entails efficiency.
    Keywords: Networks, Connections model, Heterogeneity, Efficiency, Stability.
    JEL: A14 C72 D85
    Date: 2021–05–17
  16. By: Huang, Shao'an; Qiu, Zhigang; Wang, Gaowang; Wang, Xiaodan
    Abstract: We develop a theoretical model of government intervention in which a government with private information trades strategically with other market participants to achieve its policy goal of stabilizing asset prices. When the government has precise information and cares much about its policy goal, both the government and the informed insider engage in reversed trading strategies, but they trade against each other. Government intervention can improve both market liquidity and price efficiency, and the effectiveness of government intervention depends crucially on the information quality of the government.
    Keywords: government intervention; trading; price stability; price efficiency
    JEL: G14 G18
    Date: 2021–05–17
  17. By: Aghadadashli, Hamid; Legros, Patrick
    Abstract: Managers have imperfect information about each other's willingness to collude and may signal this willingness through direct communication or market actions. Owners offer bonuses to managers and trade off productive effort provision, higher profits if managers coordinate on high prices, and the risk of antitrust fines if managers explicitly communicate. Our model shows that the distribution of fines between the owners and the managers is crucial for com- munication to be informative. High or low bonuses can reflect the willingness of owners to induce managers to explicitly communicate, and are red flags for corporate responsibility when collusion is supported by direct communication.
    Keywords: Antitrust fines; Collusion; communication; imperfect information; Incentive Schemes; managerial firms; oligopoly
    JEL: C79 D43 D82 K21
    Date: 2020–09
  18. By: Fernando Tohmé (Universidad Nacional del Sur - Conicet)
    Date: 2020–07
  19. By: Gomes, Renato; Lozachmeur, Jean-Marie; Maestri, Lucas
    Abstract: We study oligopolistic competition by firms engaging in second-degree price discrimination. In line with the large empirical literature on demand estimation, our theory allows for comovements between consumers' taste for quality and propensity to switch brands. If low-type consumers are sufficiently less (more) brand loyal than high types, (i) quality provision is inefficiently low at the bottom (high at the top) of the product line, and (ii) informational rents are negative (positive) for high types, while positive (negative) for low types. We produce several testable comparative statics on pricing and quality provision, and show that more competitive markets (in the sense that consumers are less brand-loyal) may produce lower welfare. Interestingly, pure-strategy equilibria fail to exist whenever brand loyalty is sufficiently different across consumers types. Accordingly, our theory identifies a new rationale for price/quality dispersion; namely, the interplay between self-selection constraints and heterogeneity in brand loyalty.
    Keywords: asymmetric information; Competition; preference correlation; price discrimination; price dispersion
    JEL: D82
    Date: 2020–09
  20. By: Javier Donna (University of Florida); Pedro Pereira (Autoridade da Concorrência); Andre Trindade (FGV EPGE); Renan Yoshida (Stanford Uiversity)
    Abstract: Cutting out the intermediary and selling directly to consumers is an increasingly common strategy by manufacturers in many industries. We develop a structural model of vertical relations where manufacturers both bargain with retailers over wholesale prices and sell their products directly to consumers. We show that direct sales by manufacturers generate two effects that have opposing impact on welfare. First, direct sales generate potential welfare gains to consumers downstream due to additional competition and product variety. Second, in the upstream, there is an increase in the bargaining leverage of the manufacturers selling directly to consumers. Negotiated wholesale prices increase, thus increasing final prices to consumers and decreasing consumer welfare. We show how our model can be used to quantify the bargaining leverage and welfare effects of direct sales. We estimate our model using data from the outdoor advertising industry and use the estimated model to simulate counterfactual scenarios to isolate these effects. We conclude by discussing the relevance of the bargaining leverage effect for vertical merger evaluation.
    Keywords: Direct-to-consumer sales, bargaining, vertical mergers, advertising
    JEL: D43 L13 L42 L51 L81 M37
    Date: 2021–05
  21. By: Benoit S Y Crutzen (Erasmus School of Economics); Hideo Konishi (Boston College); Nicolas Sahuguet (HEC Montreal)
    Abstract: Under closed-list proportional representation, a party's electoral list determines the order in which legislative seats are allocated to candidates. When candidates differ in their ability, parties face a trade-off between competence and incentives. Ranking candidates in decreasing order of competence ensures that elected politicians are most competent. Yet, party lists create incentives for candidates that may push parties not to rank candidates in decreasing competence order. We examine this trade-off in a game-theoretical model in which parties rank their candidate on a list, candidates choose their campaign effort, and the election is a team contest for multiple prizes. We show that the trade-off between competence and incentives depends on candidatesÂ’' objective and the electoral environment. In particular, parties rank candidates in decreasing order of competence if candidates value enough post-electoral high offices or media coverage focuses on candidates at the top of the list.
    JEL: D72 C72
    Date: 2021–05–10

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