nep-gth New Economics Papers
on Game Theory
Issue of 2020‒07‒27
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Robust communication on networks By Marie Laclau; Ludovic Renou; Xavier Venel
  2. Expectational Equilibria in Many-to-one Matching Models with Contracts - A Reformulation of Competitive Equilibrium By Herings, P. Jean-Jacques
  3. Algorithm for Computing Approximate Nash equilibrium in Continuous Games with Application to Continuous Blotto By Sam Ganzfried
  4. Quantile Analysis of "Hazard-Rate" Game Models By Enache, Andreea; Florens, Jean-Pierre
  5. Social Welfare in Search Games with Asymmetric Information By Gilad Bavly; Yuval Heller; Amnon Schreiber
  6. Repeated Communication with Private Lying Cost By Harry Pei
  7. Intelligence, Errors and Strategic Choices in the Repeated Prisoners' Dilemma By Proto, Eugenio; Rustichini, Aldo; Sofianos, Andis
  8. The Value of Information in Zero-Sum Games By Olivier GOSSNER; Jean-François MERTENS
  9. Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment By Harry Pei
  10. Mean Field Exponential Utility Game: A Probabilistic Approach By Guanxing Fu; Xizhi Su; Chao Zhou
  11. Biased-Belief Equilibrium By Yuval Heller; Eyal Winter
  12. Environmental markets exacerbate inequalities By Ambec, Stefan
  13. Coalition-Proof Risk Sharing Under Frictions By Cole, Harold; Krueger, Dirk; Mailath, George J; Park, Yena
  14. Unraveling of Value-Rankings in Auctions with Resale By Sanyyam Khurana
  15. Corona Games: Masks, Social Distance and Mechanism Design By Balazs Pejo; Gergely Biczok
  16. Dynamic games applied to common resources: modeling and experimentation By Anmina Murielle Djiguemde; Dimitri Dubois; Mabel Tidball; Alexandre Sauquet
  17. Estimation of (static or dynamic) games under equilibrium multiplicity By Otsu, Taisuke; Pesendorfer, Martin; Sasaki, Yuya; Takahashi, Yuya
  18. Double overreaction in beauty contests with information acquisition: theory and experiment By Romain Baeriswyl; Kene Boun My; Camille Cornand

  1. By: Marie Laclau; Ludovic Renou; Xavier Venel
    Abstract: We consider sender-receiver games, where the sender and the receiver are two distinct nodes in a communication network. Communication between the sender and the receiver is thus indirect. We ask when it is possible to robustly implement the equilibrium outcomes of the direct communication game as equilibrium outcomes of indirect communication games on the network. Robust implementation requires that: (i) the implementation is independent of the preferences of the intermediaries and (ii) the implementation is guaranteed at all histories consistent with unilateral deviations by the intermediaries. Robust implementation of direct communication is possible if and only if either the sender and receiver are directly connected or there exist two disjoint paths between the sender and the receiver.
    Date: 2020–07
  2. By: Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics)
    Abstract: We introduce the notion of expectational equilibrium in a very general specification of the many-to-one matching with contracts model. The endogenous variables in an expectational equilibrium are expectations about tradable contracts. Expectational equilibrium outcomes are equivalent to stable outcomes. Substitutability of preferences is a sufficient condition for existence. Expectational equilibrium unifies all the other approaches used in the literature so far, in particular Walrasian equilibrium, Drèze equilibrium, and market clearing cutoffs. It also applies to cases where contracts do not involve money as well as cases where there is a smallest monetary unit of account.
    JEL: C71 C78 D45 D51
    Date: 2020–07–02
  3. By: Sam Ganzfried
    Abstract: Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games---in which the pure strategy space is (potentially uncountably) infinite---is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for computing Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games of imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute very close approximations of Nash equilibrium strategies for this game.
    Date: 2020–06
  4. By: Enache, Andreea; Florens, Jean-Pierre
    Abstract: This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the "hazard-rate"). The goal is to use data on players’actions to recover the distribution of private information. We show that the structural parameter (the distribution of the unobservable characteristic) can be related to the reduced form parameter (the distribution of the data) through a quantile relation that avoids the inversion of the players’ strategy function. We estimate non-parametrically the density of the unobserved variables and we show that this is the solution of a well-posed inverse problem. Moreover, we prove that the density of the private information is estimated at a Vpn speed of convergence. Our results have several policy applications, including better design of auctions and public good contracts.
    Keywords: quantile estimation, well-posed inverse problems, auctions, regulation models, monotone hazard-rate
    JEL: C7 C57 C14
    Date: 2020–06
  5. By: Gilad Bavly; Yuval Heller; Amnon Schreiber
    Abstract: We consider games in which players search for a hidden prize, and they have asymmetric information about the prize location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an equilibrium that yields the first-best payoff (i.e., the highest social payoff under any strategy profile), and we characterize the first-best payoff. The results have interesting implications for innovation contests and R&D races.
    Date: 2020–06
  6. By: Harry Pei
    Abstract: I study repeated communication games between a patient sender and a sequence of receivers. The sender has persistent private information about his psychological cost of lying, and in every period, can privately observe the realization of an i.i.d. state before communication takes place. I characterize every type of sender's highest equilibrium payoff. When the highest lying cost in the support of the receivers' prior belief approaches the sender's benefit from lying, every type's highest equilibrium payoff in the repeated communication game converges to his equilibrium payoff in a one-shot Bayesian persuasion game. I also show that in every sender-optimal equilibrium, no type of sender mixes between telling the truth and lying at every history. When there exist ethical types whose lying costs outweigh their benefits, I provide necessary and sufficient conditions for all non-ethical type senders to attain their optimal commitment payoffs. I identify an outside option effect through which the possibility of being ethical decreases every non-ethical type's payoff.
    Date: 2020–06
  7. By: Proto, Eugenio; Rustichini, Aldo; Sofianos, Andis
    Abstract: A large literature in behavioral economics has emphasized in the last decades the role of individual differences in social preferences (such as trust and altruism) and in influencing behavior in strategic environments. Here we emphasize the role of attention and working memory, and show that social interactions among heterogeneous groups are likely to be mediated by differences in cognitive skills. Our design uses a Repeated Prisoner's Dilemma, and we compare rates of cooperation in groups of subjects grouped according to their IQ, with those in combined groups. While in combined groups we observe higher cooperation rates and profits than in separated groups (with consistent gains among lower IQ subjects and relatively smaller losses for higher IQ subjects), higher IQ subjects become less lenient when they are matched with lower IQ subjects than when they play separately. We argue that this is an instance of a general phenomenon, which we demonstrate in an evolutionary game theory model, where higher IQ among subjects determines -- through better working memory -- a lower frequency of errors in strategy implementation. In our data, we show that players indeed choose less lenient strategies in environments where subjects have higher error rates. The estimations of errors and strategies from the experimental data are consistent with the hypothesis and the predictions of the model.
    Keywords: Cooperation; Error in Transition; Intelligence; IQ; Repeated Prisoner's Dilemma; Strategy
    Date: 2020–01
  8. By: Olivier GOSSNER (CNRS – CREST, Institut Polytechnique de Paris and Department of Mathematics, London School of Economics); Jean-François MERTENS (CORE, Université Catholique de Louvain.)
    Abstract: We study the description and value of information in zero-sum games. We define a series of informational relations between information schemes, and show that informational equivalence classes are captured by canonical information structures. Moreover, two information schemes induce the same value in every game if and only if they are informationally equivalent.
    Date: 2020–07–06
  9. By: Harry Pei
    Abstract: I study a repeated game in which a patient player (e.g., a seller) wants to win the trust of some myopic opponents (e.g., buyers) but can strictly benefit from betraying them. Her benefit from betrayal is strictly positive and is her persistent private information. I characterize every type of patient player's highest equilibrium payoff. Her persistent private information affects this payoff only through the lowest benefit in the support of her opponents' prior belief. I also show that in every equilibrium which is optimal for the patient player, her on-path behavior is nonstationary, and her long-run action frequencies are pinned down for all except two types. Conceptually, my payoff-type approach incorporates a realistic concern that no type of reputation-building player is immune to reneging temptations. Compared to commitment-type models, the incentive constraints for all types of patient player lead to a sharp characterization of her highest attainable payoff and novel predictions on her behaviors.
    Date: 2020–06
  10. By: Guanxing Fu; Xizhi Su; Chao Zhou
    Abstract: We study an $N$-player and a mean field exponential utility game. Each player manages two stocks; one is driven by an individual shock and the other is driven by a common shock. Moreover, each player is concerned not only with her own terminal wealth but also with the relative performance of her competitors. We use the probabilistic approach to study these two games. We show the unique equilibrium of the $N$-player game and the mean field game can be characterized by a novel multi-dimensional FBSDE with quadratic growth and a novel mean-field FBSDEs, respectively. The well-posedness result and the convergence result are established.
    Date: 2020–06
  11. By: Yuval Heller; Eyal Winter
    Abstract: We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a player's beliefs about the opponent's strategy and the actual strategy. Our equilibrium condition requires that (i) each player choose a best-response strategy to his distorted belief about the opponent's strategy, and (ii) the distortion functions form best responses to one another. We obtain sharp predictions and novel insights into the set of stable outcomes and their supporting stable biases in various classes of games.
    Date: 2020–06
  12. By: Ambec, Stefan
    Abstract: Environmental markets distribute tradable rights on natural resources that are available for free on the earth such as water, biomass or clean air. In a framework where users differ solely in respect of their access to the resource, I investigate the allocation of rights that are accepted in the sense that, after trading, users obtain at least what they can achieve by sharing the resources they control. I show that, among all accepted rights, the more egalitarian ones do not allow any redistribution among users. Consequently, compared to an efficient allocation of resources, the net trading of rights always increases inequality.
    Keywords: Common-pool resources, environmental externalities, property rights, cooperative game, fairness, tradable quotas, emission permits.
    JEL: C71 D02 D63 Q28 Q38 Q58
    Date: 2020–07–03
  13. By: Cole, Harold; Krueger, Dirk; Mailath, George J; Park, Yena
    Abstract: We analyze efficient risk-sharing arrangements when coalitions may deviate. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any deviating coalition rely on a belief in future cooperation, and we treat the contracting conditions of original and deviating coalitions symmetrically. We show that better belief coordination (higher social capital) tightens incentive constraints since it facilitates both the formation of the original as well as a deviating coalition. As a consequence, the payoff of successfully formed coalitions might be declining in the degree of belief coordination and equilibrium allocations might feature resource burning or utility burning.
    Keywords: Coalitions; Limited Commitment; Risk Sharing
    JEL: E20
    Date: 2020–01
  14. By: Sanyyam Khurana (Department of Economics, Delhi School of Economics)
    Abstract: Consider a single-unit auction with resale and two risk neutral bidders. The ranking of the valuations is known to both the bidders—that is, the bidders know the identity of the highest and lowest valuation bidders. We show that, with the revelation of value-rankings, the classic result of “bid symmetrization” does not hold. Surprisingly, the bidder with the lowest valuation produces a stronger bid distribution than the bidder with the highest valuation. We also show that the revelation of value-rankings in auctions with resale asymmetrizes the bidding strategies. Finally, under restrictive assumptions, we compare seller’s and bidders’ ranking of a first-price and second-price auction.
    JEL: D44 D82
    Date: 2020–06
  15. By: Balazs Pejo; Gergely Biczok
    Abstract: Pandemic response is a complex affair. Most governments employ a set of quasi-standard measures to fight COVID-19 including wearing masks, social distancing, virus testing and contact tracing. We argue that some non-trivial factors behind the varying effectiveness of these measures are selfish decision-making and the differing national implementations of the response mechanism. In this paper, through simple games, we show the effect of individual incentives on the decisions made with respect to wearing masks and social distancing, and how these may result in a sub-optimal outcome. We also demonstrate the responsibility of national authorities in designing these games properly regarding the chosen policies and their influence on the preferred outcome. We promote a mechanism design approach: it is in the best interest of every government to carefully balance social good and response costs when implementing their respective pandemic response mechanism.
    Date: 2020–06
  16. By: Anmina Murielle Djiguemde (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, UM - Université de Montpellier); Dimitri Dubois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, CNRS - Centre National de la Recherche Scientifique); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier); Alexandre Sauquet
    Abstract: We study the exploitation behavior of two symmetrical farmers using groundwater table as in Rubio & Casino (2003), where water extraction is the only input in the production process of these farmers, and the dynamic is given by the evolution of the level of the water table. In our model, strategic interaction is introduced through extraction costs which negatively depend on the level of the water table. We made the assumption that the groundwater has a flat bottom, parallel sides, and that its natural recharge is provided by a constant and positive amount of rain. Another assumption is that farmers behave non cooperatively, by maximizing their actualized utilitarian criteria. We study this model in continuous time with an infinite horizon, and consider the equilibrium paths of the four following types of behavior : myopic, feedback, open-loop and social optimum. We also studied the same model in discrete time in order to see if our results will approch those in continuous time. Unlike some articles in the literature that find different results between continuous time and discrete time, we found that the discrete time model gives results equivalent to those of the continuous time, but with the condition that discretization in time is small enough. We test the behaviors using two different protocols in the laboratory (experimental economics) for both treatments in continuous and discrete time.
    Date: 2018–07–09
  17. By: Otsu, Taisuke; Pesendorfer, Martin; Sasaki, Yuya; Takahashi, Yuya
    Abstract: We propose a multiplicity-robust estimation method for (static or dynamic) games. The method allows for distinct behaviors and strategies across markets by treating market specific behaviors as correlated latent variables, with their conditional probability measure treated as an infinite-dimensional nuisance parameter. Instead of solving the intermediate problem which requires optimization over the infinite dimensional set, we consider the equivalent dual problem which entails optimization over only a finite-dimensional Euclidean space. This property allows for a practically feasible characterization of the identified region for the structural parameters. We apply the estimation method to newspaper market previously studied in Gentzkow et al. (2014) to characterize the identified region of marginal costs.
    Date: 2020–01
  18. By: Romain Baeriswyl; Kene Boun My; Camille Cornand
    Abstract: Central banks' disclosures, such as forward guidance, have a weaker effect on the economy in reality than that predicted in theoretical models. The present paper contributes to understanding how people pay attention and react to various sources of information. In a beauty contest with information acquisition, we show that strategic complementarities give rise to a double overreaction to public disclosures by increasing agents equilibrium level of attention, which, in turn, increases the weight assigned to the disclosures in agents' equilibrium action. A laboratory experiment provides evidence that the effect of strategic complementarities on participants' realised level of attention and realised action is qualitatively consistent with the theoretical predictions, although quantitatively weaker. Both the lack of attention to public disclosures and a limited level of reasoning by economic agents account for the weaker realised reaction. This suggests that for a central bank seeking to control the reaction to its public disclosures, it is just as important to influence information acquisition by recipients as it is to shape the information disclosures.
    Keywords: Central bank communication, information acquisition, beauty contest, overreaction
    JEL: D82 E52 D58
    Date: 2020

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