
on Game Theory 
By:  Philippe Jehiel (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  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, UCL  University College of London [London]); Erik Mohlin (Lund University [Lund], Institute for Futures Studies) 
Abstract:  We develop a framework for categorization in games, applicable both to multistage games of complete information and static games of incomplete information. Players use categories to form coarse beliefs about their opponents' behavior. Players bestrespond given these beliefs, as in analogybased expectations equilibria. Categories are related to previously used strategies via the requirements that categories contain a sufficient amount of observations and exhibit sufficient withincategory similarity, in line with the biasvariance tradeoff. When applied to classic games including the chainstore game and adverse selection games our framework yields less unintuitive predictions than those arising with standard solution concepts. 
Keywords:  Bounded rationality, Categorization, Biasvariance tradeoff, Adverse selection, Chainstore paradox 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs04154272&r=gth 
By:  Johannes Treutlein 
Abstract:  Evidential cooperation in large worlds (ECL) refers to the idea that humans and other agents can benefit by cooperating with similar agents with differing values in causally disconnected parts of a large universe. Cooperating provides agents with evidence that other similar agents are likely to cooperate too, resulting in gains from trade for all. This could be a crucial consideration for altruists. I develop a gametheoretic model of ECL as an incomplete information bargaining problem. The model incorporates uncertainty about others' value systems and empirical situations, and addresses the problem of selecting a compromise outcome. Using the model, I investigate issues with ECL and outline open technical and philosophical questions. I show that all cooperators must maximize the same weighted sum of utility functions to reach a Pareto optimal outcome. However, I argue against selecting a compromise outcome implicitly by normalizing utility functions. I review bargaining theory and argue that the Nash bargaining solution could be a relevant Schelling point. I introduce dependency equilibria (Spohn 2007), an equilibrium concept suitable for ECL, and generalize a folk theorem showing that the Nash bargaining solution is a dependency equilibrium. I discuss gains from trade given uncertain beliefs about other agents and analyze how these gains decrease in several toy examples as the belief in another agent decreases. Finally, I discuss open issues in my model. First, the Nash bargaining solution is sometimes not coalitionally stable, meaning that a subset of cooperators can unilaterally improve payoffs by deviating from the compromise. I investigate conditions under which stable payoff vectors exist. Second, I discuss how to model agents' default actions without ECL. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.04879&r=gth 
By:  Gentry, Matthew; Pesendorfer, Martin 
Abstract:  A singleproduct retailer faces bargain hunting consumers whose willingness to pay incorporates sensations of gain and loss driven by differences between the observed price and prices they rationally expect in the spirit of Koszegi and Rabin (2006). We examine the Bayesian Nash equilibrium (noncommitment) pricing solution in which (i) the retailer maximizes profit given consumers' beliefs and (ii) consumers' beliefs are consistent with the retailer's choice. We show two novel results: First, a purestrategy, uniformprice, equilibrium does not exist when consumers are bargain hunters who value gains more than losses. Second, in this case there exists a mixed strategy equilibrium and all mixed strategy equilibria involve the same retailer profit. The equilibrium retailer profit is (weakly) lower than in the absence of reference effects. 
Keywords:  bargain hunting; pricing; reference effects 
JEL:  J1 
Date:  2021–09–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:111591&r=gth 
By:  Olivier Compte 
Abstract:  Motivated by the idea that lack of experience is a source of errors but that experience should reduce them, we model agents' behavior using a stochastic choice model, leaving endogenous the accuracy of their choice. In some games, increased accuracy is conducive to unstable bestresponse dynamics. We define the barrier to learning as the minimum level of noise which keeps the bestresponse dynamic stable. Using logit Quantal Response, this defines a limitQR Equilibrium. We apply the concept to centipede, travelers' dilemma, and 1120 moneyrequest games and to firstprice and allpay auctions, and discuss the role of strategy restrictions in reducing or amplifying barriers to learning. 
Date:  2023–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2306.16904&r=gth 
By:  Itai Arieli (Technion  Israel Institute of Technology); Ivan Geffner (Technion  Israel Institute of Technology); Moshe Tennenholtz (Technion  Israel Institute of Technology) 
Abstract:  In an information aggregation game, a set of senders interact with a receiver through a mediator. Each sender observes the state of the world and communicates a message to the mediator, who recommends an action to the receiver based on the messages received. The payoff of the senders and of the receiver depend on both the state of the world and the action selected by the receiver. This setting extends the celebrated cheap talk model in two aspects: there are many senders (as opposed to just one) and there is a mediator. From a practical perspective, this setting captures platforms in which strategic experts advice is aggregated in service of action recommendations to the user. We aim at finding an optimal mediator/platform that maximizes the users' welfare given highly resilient incentive compatibility requirements on the equilibrium selected: we want the platform to be incentive compatible for the receiver/user when selecting the recommended action, and we want it to be resilient against group deviations by the senders/experts. We provide highly positive answers to this challenge, manifested through efficient algorithms. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.05054&r=gth 
By:  Bingyan Han; Chi Seng Pun; Hoi Ying Wong 
Abstract:  This paper studies robust timeinconsistent (TIC) linearquadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a timeconsistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust meanvariance analysis, namely with state and controldependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems. 
Date:  2023–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2306.16982&r=gth 
By:  Krishnamurthy Iyer; Haifeng Xu; You Zu 
Abstract:  We consider a dynamic Bayesian persuasion setting where a single longlived sender persuades a stream of ``shortlived'' agents (receivers) by sharing information about a payoffrelevant state. The state transitions are Markovian and the sender seeks to maximize the longrun average reward by committing to a (possibly historydependent) signaling mechanism. While most previous studies of Markov persuasion consider exogenous agent beliefs that are independent of the chain, we study a more natural variant with endogenous agent beliefs that depend on the chain's realized history. A key challenge to analyze such settings is to model the agents' partial knowledge about the history information. We analyze a Markov persuasion process (MPP) under various information models that differ in the amount of information the receivers have about the history of the process. Specifically, we formulate a general partialinformation model where each receiver observes the history with an $\ell$ period lag. Our technical contribution start with analyzing two benchmark models, i.e., the fullhistory information model and the nohistory information model. We establish an ordering of the sender's payoff as a function of the informativeness of agent's information model (with nohistory as the least informative), and develop efficient algorithms to compute optimal solutions for these two benchmarks. For general $\ell$, we present the technical challenges in finding an optimal signaling mechanism, where even determining the right dependency on the history becomes difficult. To bypass the difficulties, we use a robustness framework to design a "simple" \emph{historyindependent} signaling mechanism that approximately achieves optimal payoff when $\ell$ is reasonably large. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.03181&r=gth 
By:  Philippe Jehiel (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  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 PanthéonSorbonne  ENSPSL  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, UCL  University College of London [London]); Giacomo Weber (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  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 PanthéonSorbonne  ENSPSL  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:  Families of normalform twoplayer games are categorized by players into K analogy classes applying the Kmeans clustering technique to the data generated by the distributions of opponent's behavior. This results in Calibrated AnalogyBased Expectation Equilibria in which strategies are analogybased expectation equilibria given the analogy partitions and analogy partitions are derived from the strategies by the Kmeans clustering algorithm. We discuss various concepts formalizing this, and observe that distributions over analogy partitions are sometimes required to guarantee existence. Applications to games with linear bestresponses are discussed highlighting the differences between strategic complements and strategic substitutes. 
Keywords:  Kmean clustering, Analogybased Expectation Equilibrium Kmean clustering 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs04154234&r=gth 
By:  Benjamin Ouvrard (GAEL  Laboratoire d'Economie Appliquée de Grenoble  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement  UGA  Université Grenoble Alpes  Grenoble INP  Institut polytechnique de Grenoble  Grenoble Institute of Technology  UGA  Université Grenoble Alpes); Arnaud Reynaud (TSER  Toulouse School of Economics  UT Capitole  Université Toulouse Capitole  UT  Université de Toulouse  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Stéphane Cezera (TSER  Toulouse School of Economics  UT Capitole  Université Toulouse Capitole  UT  Université de Toulouse  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Alban Thomas (UMR PSAE  ParisSaclay Applied Economics  AgroParisTech  Université ParisSaclay  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, US ODR  Observatoire des Programmes Communautaires de Développement Rural  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Dishant Jojit James (Wyzsza Szkola Bankowa University); Murudaiah Shivamurthy (Department of Agricultural Extension, GKVK, UAS, Bangalore) 
Abstract:  We use a framedfield experiment to analyze the preferences of Indian farmers regarding water sharing. Farmers play a dictator game (DG) behind the veil of ignorance in which a limited quantity of water has to be allocated between two farmers. We vary the equity/efficiency tradeoff by introducing some heterogeneity between farmers' productivity and by considering an upstream/downstream spatial configuration. We first show that generosity in the DG is high (on average, respectively 44% and 47% of the total quantity of water or the total profit are left by the dictator). Only a small proportion of farmers act in the DG as selfish profit maximizers, a majority of them adopting efficient, egalitarian in payoff or egalitarian in quantity behaviors. We then show that it is possible to induce more efficient water allocation behaviors in the DG by modifying farmer's choice architecture. A loss framing induces farmers to share more efficiently the water resource, but only when the most productive farmer is located downstream. On the contrary, we find mild evidence that farmers choose less often the efficient solution with a gain framing. 
Keywords:  Dictator Game, Framedfield experiment, Framing, Water sharing 
Date:  2023–07–04 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal04150233&r=gth 
By:  Nicola Campigotto; Marco Catola; Simone D’Alessandro; Pietro Guarnieri; Lorenzo Spadoni 
Abstract:  This paper explores the potential of voluntary consumption quotas as a strategy to address resource supply shortages. The results of an incentivized online experiment are presented in which a Nash demand game was used to model an energy consumption problem. Participants had the option to join an energy conservation programme by accepting a consumption quota. Those who accepted the quota traded off their maximum demand for energy in exchange for the certainty that their demand would be met, while those who rejected the quota could demand and possibly earn more but risked suffering from a power outage, in which case they received nothing. Three different quota schemes are examined, and their policy implications are discussed. Our findings suggest that voluntary quotas may lead to a significant decrease in overall demand and contribute to enhancing consumption security. 
Keywords:  energy consumption, online experiment, Nash demand game, power outages, voluntary quotas 
JEL:  C72 C99 Q48 
Date:  2023–07–01 
URL:  http://d.repec.org/n?u=RePEc:pie:dsedps:2023/299&r=gth 
By:  Mignot, Sarah; Tramontana, Fabio; Westerhoff, Frank H. 
Abstract:  We develop a nonlinear duopoly model in which the heuristic expectation formation and learning behavior of two boundedly rational firms may engender complex dynamics. Most importantly, we assume that the firms employ different forecasting models to predict the behavior of their opponent. Moreover, the firms learn by leaning more strongly on forecasting models that yield more precise predictions. An eightdimensional nonlinear map drives the dynamics of our approach. We analytically derive the conditions under which its unique steady state is locally stable and numerically study its outofequilibrium behavior. In doing so, we detect multiple scenarios with coexisting attractors at which the firms' behavior yields distinctively different market outcomes. 
Keywords:  Duopoly model, heuristic expectation formation, learning behavior, nonlinear dynamics, stability and bifurcation analysis, coexisting attractors 
JEL:  C73 D43 L12 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:zbw:bamber:187&r=gth 
By:  Tirole, Jean; Moisson, PaulHenri; Dubois, Pierre 
Abstract:  It is puzzling that cooperatives, which stand for the interests of their users, do not occupy more space in the market for corporate forms. This paper unveils a new impediment to their formation. It shows that equilibrium freeriding handicaps cooperatives in their competition with alternative institutions, notably the forprofits. The irrelevance of cooperatives is a remarkably robust result. The paper then analyzes desirable government interventions in the corporate market. 
Keywords:  Cooperatives; freeriding; competing corporate forms 
JEL:  D23 D71 D8 L22 
Date:  2023–07–03 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:128186&r=gth 
By:  Qian Lei; Chi Seng Pun 
Abstract:  This paper studies the wellposedness of a class of nonlocal parabolic partial differential equations (PDEs), or equivalently equilibrium HamiltonJacobiBellman equations, which has a strong tie with the characterization of the equilibrium strategies and the associated value functions for timeinconsistent stochastic control problems. Specifically, we consider nonlocality in both time and space, which allows for modelling of the stochastic control problems with initialtimeandstate dependent objective functionals. We leverage the method of continuity to show the global wellposedness within our proposed Banach space with our established Schauder prior estimate for the linearized nonlocal PDE. Then, we adopt a linearization method and Banach's fixed point arguments to show the local wellposedness of the nonlocal fully nonlinear case, while the global wellposedness is attainable provided that a very sharp apriori estimate is available. On top of the wellposedness results, we also provide a probabilistic representation of the solutions to the nonlocal fully nonlinear PDEs and an estimate on the difference between the value functions of sophisticated and na\"{i}ve controllers. Finally, we give a financial example of time inconsistency that is proven to be globally solvable. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.01986&r=gth 