
on Game Theory 
By:  Sam Ganzfried 
Abstract:  In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are twoplayer nonzerosum with 3 pure strategies per player. Shapley assumed that each player played a specific pure strategy in the first round. We show that if we use random (mixed) strategy profile initializations we are able to converge to Nash equilibrium approximately 1/3 of the time for a representative game in this class. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.02154&r= 
By:  Alex Centeno; Leidy Garc\'ia 
Abstract:  The objective of this paper is to identify and analyze the response actions of a set of partially rational players embedded in subnetworks in the context of social interaction and learning. We characterize strategic network formation as a static game of interactions with incomplete information, where players maximize their utility depending on the connections they establish and multiple interdependent actions that permit groupspecific parameters of players. It is challenging to apply this type of model to reallife scenarios for two reasons: The computation of the Bayesian Nash Equilibrium is highly demanding and the identification of social influence requires the use of excluded variables that are oftentimes unavailable. Based on the theoretical proposal, we propose a set of simulant equations and discuss the identification of the social interaction effect employing multimodal network autoregressive. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.08380&r= 
By:  Qian Chen; Chenwei Shi; Yiyan Wang 
Abstract:  This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of LPFD and HLPFD to modelling cooperative games in strategic and coalitional forms is explored. The resulted framework provides a unified view on Nash equilibrium, Pareto optimality and the core. The philosophical relevance of these gametheoretical notions to discussions of collective agency is made explicit. Some key connections with other logics are also revealed, for example, the coalition logic, the logic functional dependence and the logic of ceteris paribus preference. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.08213&r= 
By:  Emiliano Catonini; Antonio Penta 
Abstract:  Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete information (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rationalizability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incompleteinformation extension of subgame consistency (continuationgame consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis. We also discuss a few applications, including a new version of peerconfirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings. 
Keywords:  backward induction, backwards procedure, backwards rationalizability, Incomplete Information, interim perfect equilibrium, Rationalizability, robustness 
JEL:  C72 C73 D82 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:1315&r= 
By:  Deepanshu Vasal 
Abstract:  In this paper, we consider a discretetime Stackelberg graphon mean field game with a finite number of leaders, a finite number of major followers and an infinite number of minor followers. The leaders and the followers each observe types privately that evolve as conditionally independent controlled Markov processes. The leaders and the followers sequentially make strategic decisions where each follower's actions affect her neighbors, which is captured in a graph generated by a known graphon, however, the leaders' actions affect everyone. The leaders are of "Stackelberg" kind which means each of them commits to a dynamic policy and all the followers(both major and minor) best respond to that policy and each other. Knowing that the minor followers would best respond (in the sense of a meanfield game) while the major followers will best respond (in the sense of NAsh) based on their policies, each leader chooses a policy that maximizes her reward knowing that other leader's are doing the same. We refer to the resulting outcome as a Stackelberg Graphon Mean Field Equilibrium with multiple leaders (SGMFEML). In this paper, we provide a master equation of this game that allows one to compute all SGMFEML. We further extend this notion to the case when there are an infinite number of leaders. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.03186&r= 
By:  Mehmet S. Ismail 
Abstract:  There are two wellknown sufficient conditions for Nash equilibrium: common knowledge of rationality, and common prior, which exogenously assumes a profile of beliefs that are correct. However, it is not known how players arrive at a common prior \textit{before} playing the original game. In this note, I assume, in addition to (objective and subjective) rationality, that players' beliefs \textit{will be} correct once the game is played, but a common prior is not assumed. I study whether and under what conditions players endogenously arrive at a common prior. The main finding is an impossibility theorem, which states that mutual knowledge of rationality and mutual knowledge of correct beliefs are not in general logically consistent in $n$person games. However, the two assumptions are consistent in twoplayer zerosum games. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.09847&r= 
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]); Larry Samuelson (Yale University [New Haven]) 
Abstract:  We offer an approach to cooperation in repeated games of private monitoring in which players construct models of their opponents' behavior by observing the frequencies of play in a record of past plays of the game in which actions but not signals are recorded. Players construct models of their opponent's behavior by grouping the histories in the record into a relatively small number of analogy classes to which they attach probabilities of cooperation. The incomplete record and the limited number of analogy classes lead to misspecified models that provide the incentives to cooperate. We provide conditions for the existence of equilibria supporting cooperation and equilibria supporting high payoffs for some nontrivial analogy partitions. 
Keywords:  Analogical reasoning,Cooperation,Prisoners' dilemma,Repeated game,Private monitoring Analogical reasoning,Private monitoring 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03754101&r= 
By:  Longjian Li 
Abstract:  This paper explores how ambiguity affects communication. We consider a cheap talk model in which the receiver evaluates the sender's message with respect to its worstcase expected payoff generated by multiplier preferences. We characterize the receiver's optimal strategy and show that the receiver's posterior action is consistent with his exante action. We find that in some situations, ambiguity improves communication by shifting the receiver's optimal action upwards, and these situations are not rare. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.08494&r= 
By:  Michele Bee (CEDEPLAR/UFMG); Juan Pablo Gama (CEDEPLAR/UFMG) 
Abstract:  We propose a theoretical representation of how agents estimate demand through a market learning process. To this end, we model a traditional marketplace by interpreting Smith’s theory of the convergence of the market price to the natural price, understood as the reserve price. In this model, natural price is obtained through a bargaining process between consumers and producers. We use a repeated multiperiod game with producers deciding their offers and both, consumers and producers, in an imperfect type of competition. Producers estimate the demand at the reserve price thanks to information provided by competition as rivalry between consumers and between producers. But the stronger this competition is, the slower the discovery process. 
Keywords:  Demand discovery, natural price, rivalry, imperfect competition 
JEL:  B12 C72 C73 D43 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:cdp:texdis:td647&r= 
By:  Alan Hammond 
Abstract:  We introduce a twoperson nonzerosum randomturn game that is a variant of the stakegoverned games introduced recently in [HP2022]. We call the new game the Trail of Lost Pennies. At time zero, a counter is placed at a given integer location: $X_0 = k \in \mathbb{Z}$, say. At the $i$th turn (for $i \in \mathbb{N}_+$), Maxine and Mina place nonnegative stakes, $a_i$ and $b_i$, for which each pays from her own savings. Maxine is declared to be the turn victor with probability $\tfrac{a_i}{a_i+b_i}$; otherwise, Mina is. If Maxine wins the turn, she will move the counter one place to the right, so that $X_i = X_{i1} +1$; if Mina does so, the counter will move one place to the left, so that $X_i = X_{i1} 1$. If $\liminf X_i = \infty$, then Maxine wins the game; if $\limsup X_i = \infty$, then Mina does. (A special rule is needed to treat the remaining, indeterminate, case.) When Maxine wins, she receives a terminal payment of $m_\infty$, while Mina receives $n_\infty$. If Mina wins, these respective receipts are $m_{\infty}$ and $n_{\infty}$. The four terminal payment values are supposed to be real numbers that satisfy $m_\infty > m_{\infty}$ and $n_\infty 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.07451&r= 
By:  Malte Baader; Simon Gaechter; Kyeongtae Lee; Martin Sefton 
Abstract:  We experimentally examine how the incentive to defect in a social dilemma affects conditional cooperation. In our first study we conduct online experiments in which subjects play eight Sequential Prisoner’s Dilemma games with payoffs systematically varied across games. We find that few second movers are conditionally cooperative (i.e., cooperate if and only if the first mover cooperates) in all eight games. Instead, most secondmovers change strategies between games. The rate of conditional cooperation is higher when the own gain from defecting is lower and when the loss imposed on the first mover from defecting is higher. This pattern is consistent with both social preference models and stochastic choice models. To explore which model explains our findings we employ a second study to jointly estimate noise and social preference parameters at the individual level. The majority of our subjects place significantly positive weight on others’ payoffs, supporting the underlying role of social preferences in conditional cooperation. 
Keywords:  sequential prisoner’s dilemma, conditional cooperation, social preferences 
JEL:  A13 C91 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9924&r= 
By:  Ay?e Gül Mermer (Tilburg University); Sander Onderstal (University of Amsterdam); Joep Sonnemans (University of Amsterdam) 
Abstract:  In economic environments, decisionmakers may strategically delay irreversible investments to learn from the actions of others creating socially suboptimal outcomes. We investigate if and how communication mitigates the strategic delay in investment timings. Players choose when to invest in a nonrival project with uncertain returns. The earliest investor bears the costs of investment and all players learn whether the project is of good or bad quality. Informational externalities create freeriding incentives resulting in strategic delays in investment timings. Our theoretical analysis suggests that introducing communication into this setting reduces strategic delay. We implement our model in a laboratory experiment utilizing a 2x2 design, where we vary the availability of communication and the number of agents. We find that communication significantly reduces the strategic delay and leads to earlier investment timings in the twoplayer case. In the case of four players, communication helps subjects to coordinate and reduce strategic delay significantly in the first period of the experiment, while coordination failures emerge in the following periods sweeping away the beneficial effect of communication at the aggregate level. 
Keywords:  Investment Timing, Strategic Delay, Communication, Coordination, Informational, Externalities, Experiments 
JEL:  C71 C92 D83 L40 
Date:  2022–09–20 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:202200065&r= 
By:  Mariann Ollár; Antonio Penta 
Abstract:  We study efficient implementation via transfers in unique rationalizable strategies, in environments that are symmetric in two senses: first, agents display the same total level of preference interdependence; second, types are commonly known to be drawn from distributions with identical (but unknown) means. We characterize the conditions under which full efficient implementation is possible via direct mechanisms, as well as the transfer schemes which achieve it whenever possible. We discuss a further robustness property, robustness to mistaken play, and show that it uniquely selects the transfer scheme which induces an even redistribution of strategic externalities. 
Keywords:  efficient implementation, full implementation, interdependent values, loading transfers, equalexternality transfers, Rationalizability, robustness, sensitivity analysis, strategic externalities, symmetric environments, uniqueness 
JEL:  D62 D82 D83 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:1311&r= 
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]); Erik Mohlin (Lund University [Lund], Institute for Futures Studies) 
Abstract:  We study learning in a decentralized pairwise adverse selection economy, where buyers have access to the quality of traded goods but not to the quality of nontraded goods. Buyers categorize ask prices in order to predict quality as a function of ask price. The categorization is endogenously determined so that outcomes that are observed more often are categorized more finely, and within each category beliefs reflect the empirical average. This leads buyers to have a very fine understanding of the relationship between qualities and ask prices for prices below the current market price, but only a coarse understanding above that price. We find that this induces a price cycle involving the Nash equilibrium price, and one or more higher prices. 
Keywords:  Adverse selection,Bounded rationality,Categorization,Learning,Model misspeciÖcation,OTC markets Adverse selection,Model misspecification,OTC markets 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03754118&r= 
By:  Dongkyu Chang; Duk Gyoo Kim; Wooyoung Lim 
Abstract:  We consider infinitehorizon bargaining in which an uninformed seller sequentially makes a price offer to a privately informed buyer who decides whether to accept or reject it in every bargaining round. Existing theories suggest that the presence (absence) of an arbitrarily small outside option available to the buyer in this dynamic screening problem leads the seller (buyer) to enjoy a substantial surplus, and we examine the validity of the differences in the share of the surplus theoretically and experimentally. We first show that the theoretical differences collapse if an arbitrarily small fraction of optimistic buyers would believe that the sellers sometimes ask for a lower price in the subsequent rounds. We then present experimental evidence that the earnings of both the buyers and the sellers when the buyer has an outside option are not significantly different from those without the outside option. We find supporting evidence that some buyers reject the currentround offers, optimistically believing that the next offer would be more favorable to them. 
Keywords:  positive selection, outside options, laboratory experiments 
JEL:  C78 C91 D03 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9908&r= 
By:  Schmitt, Stefanie Y. 
Abstract:  I analyze the implication of consumers' limited attention to quality differences on market outcomes and welfare. I model this limited attention to quality differences with a perception threshold: Consumers only perceive quality differences between goods that exceed the consumers' perception threshold. The model allows for two types of equilibria: equilibria with distinguishable and equilibria with indistinguishable qualities. I show that horizontal product differentiation, which gives firms market power, affects equilibrium selection. If firms are horizontally differentiated, firms produce goods with indistinguishable qualities. Then, limited attention harms consumers and benefits firms. In contrast, if firms are not horizontally differentiated, firms produce goods with distinguishable qualities. Then, limited attention has no effect on consumers' welfare or firms' profits. 
Keywords:  Limited Attention,Perception Threshold,Product Differentiation,Product Quality 
JEL:  D43 D91 L13 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:bamber:184&r= 
By:  Rötzer, Sebastian 
Abstract:  I propose a novel mechanism of how common ownership affects product market competition. Internalization of shareholders' portfolio interests into managers' objective functions is no longer necessary if owners can provide active monitoring that affects firms' ability to compete. Whenever product market externalities cause common owners to neglect monitoring, firms are less competitive compared to a counterfactual where shareholder interests are aligned with firm value maximization. I formally prove this intuition in a static model of active monitoring with common ownership that allows for heterogeneous firms and portfolio allocations. Based on the game's unique Nash equilibrium, I derive empirical predictions that link unobserved active monitoring to observed product market outcomes. I conclude with a brief analysis of two policy interventions aimed at curbing the anticompetitive effects of common ownership. 
Keywords:  Common ownership, corporate governance, industrial organization, product markets 
JEL:  G34 L13 
Date:  2022–08–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:114560&r= 
By:  Luisa Montanari; Ulrike SchmidtKraepelin; Warut Suksompong; Nicholas Teh 
Abstract:  We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envybased notions cannot be extended to the case where agents have matroidrank (i.e., binary submodular) valuations. We propose two families of envybased notions for matroidrank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroidrank valuations. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.06437&r= 
By:  Sergiu Hart 
Abstract:  A formal writeup of the simple proof (1995) of the existence of calibrated forecasts by the minimax theorem, which moreover shows that N^3 periods suffice to guarantee a 1/N calibration error. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.05863&r= 