Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

Interconnected games and international environmental problems

The purpose of this paper is to introduce the concept of interconnected games and to show its relevance for modeling international environmental problems. It is argued that an interconnected game approach to international environmental problems may enhance cooperation and provide an alternative to the use of financial side payments to induce countries to cooperate. Two types of interconnected games are distinguished in this paper, i.e. direct sum games and tensor games. In the former all the constituting isolated games are games in strategic form and in the latter they are repeated games. In both cases the interconnected game can be interpreted as a multiple objective game, but only the setting where a trade-off is made for the vector-payoffs is considered. In addition to the formal definition of these types of interconnected games, some elementary results concerning Nash equilibria of such games are derived.Folmer and v. Mouche: Landbouwuniversiteit Wageningen, Postbus 8130, 6700 EW Wageningen, The Netherlands; Ragland: University of Colorado at Boulder, Boulder, Colorado 80309-0256, U.S.A. An earlier version of this paper was presented at the EAERE conference in Stockholm, June 1991. The authors appreciate comments made by conference participants and journal referees.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

The convergence of equilibrium strategies of approximating signaling games

Summary For a class of infinite signaling games, the perfect Bayesian equilibrium strategies of finite approximating games converge to equilibrium strategies of the infinite game. This proves the existence of perfect Bayesian equilibrium for that class of games. It is well known that in general, equilibria may not exist in infinite signaling games.I am very grateful to Karl Iorio with whom I derived most of the results in this paper. I am solely responsible for any remaining errors. I am also grateful to Robert Anderson, Debra Aron, Eddie Dekel, Raymond Deneckere, Michael Kirscheneiter, Steven Matthews, Roger Myerson, Daniel Vincent and Robert Weber for comments on previous drafts of this paper.     

VIDEO GAMES AND CRIME

Psychological studies find that video game play is associated with markers for violent and antisocial attitudes. It is plausible that these markers indicate either whetted or sated preferences for antisocial behavior. I investigate whether a proxy for video gaming is associated with the prevalence of various crimes and find evidence that gaming is associated with significant declines in crime and death rates. These results are robust to various alternative specifications. Other youth‐related leisure activities—sports and movie viewing—generate smaller or no effects. These results cast doubt on the desirability of proposed restrictions on video game marketing. (JEL L86, D18, I18)     

Playing the wrong game: An experimental analysis of relational complexity and strategic misrepresentation

It has been suggested that players often produce simplified and/or misspecified mental models of strategic decisions [Kreps, D., 1990. Game Theory and Economic Modeling. Oxford Univ. Press, Oxford]. We submit that the relational structure of players' preferences in a game is a source of cognitive complexity, and may be an important driver of such simplifications. We provide a classification of order structures in two-person games based on the properties of monotonicity and projectivity, and present experiments in which subjects construct representations of games of different relational complexity and subsequently play the games according to these representations. Experimental results suggest that relational complexity matters. More complex games are harder to represent, and this difficulty seems correlated with short term memory capacity. In addition, most erroneous representations are simpler than the correct ones. Finally, subjects who misrepresent the games behave consistently with such representations, suggesting that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises.     

ADOLESCENT VIDEO GAME PLAYING AND FIGHTING OVER THE LONG‐TERM

I present new evidence of the link between video game play and fighting. The General Learning Model predicts that increased aggression from playing violent video games. These predictions are tested using a large longitudinal data set tracking adolescents over time. Consistent with previous research, there is a positive raw correlation between video game playing as an adolescent and aggressive outcomes, in this case fights, even more than a decade later. However, multivariate and instrumental variables estimators do not find a causal relationship. Some implications are: support policy for further interventions is undermined, future research should be more careful about identification threats, and similar methodological approaches can be applied to the effects of other new communication technologies. (JEL D18, L86, O35)     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Modelling International Policy Games: Lessons from European Monetary Coordination

Most international monetary policy games are modelled as prisoners' dilemma games. Political scientists suggest however that other game-theoretic structures (chicken, stag-hunt and deadlock games) could be more appropriate to describe international monetary coordination. This paper provides some empirical evidence on this issue, by studying the case of European monetary coordination from 1979 to 1989. First, central banks' and governments' preferences are revealed through an analysis of their actual behaviour. Then, the dynamic game describing policymakers' interactions is simulated under alternative institutional arrangements: coordination, defection, sub-group coalitions, etc. The main conclusion is that the stylised facts derived from those experiments seem not to be consistent with the implications of the prisoners' dilemma framework. Consistency is instead found with the features of a stag-hunt game. CEPR and FEEM This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9.     

Equilibrium in behavior strategies in infinite extensive form games with imperfect information

Summary We prove the existence of equilibrium in behavior strategies for extensive form games when the game has infinite actions. The result is derived under the assumption that the behavior strategies satisfy the bounded measurability condition. The condition implies that the behavior strategies are restricted to those which can be viewed as continuous functions from the set of initial histories to the space of probability distributions over action spaces which satisfy the Lipschitz bound.I am grateful for the helpful comments of an anonymous referee.     

Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility, and demonstrate conditions ensuring that a game with limited side payments has a nonempty -core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed and large transfers are prohibited, then all payoffs in the -core treat similar players similarly. A bound on the distance between -core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that games with many players and small effective groups have the properties of competitive markets. Journal of Economic Literature Classification Numbers: C71, C78, D71.     

Reciprocity, Trust, and Payoff Privacy in Extensive Form Bargaining

We report decision making in two-person extensive form game trees, using six treatments that vary matching protocol, payoffs, and payoff information. Our objective is to examine game theoretic hypotheses of decision making based on dominance and backward induction in comparison with the culturally or biologically derived hypothesis that reciprocity supports more cooperation than predicted by game theory. We find strong support for cooperation under complete information, even in single-play treatments and in games of trust, unreinforced by the prospect of punishment for defection from reciprocity. Only under private information do we observe strong support for noncooperative game theory.Journal of Economic LiteratureClassification Numbers: C78, C92.     

Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games

The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between quasi-submodularity and global evolutionary stability of strategies for these games, which – apart from being of independent interest – accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy of a quasi-submodular aggregative game must also be globally stable. That is, if one mutant cannot successfully invade a population, any number of mutants can do so even lessThe author is grateful to Ana Ania and Carlos Alōs-Ferrer for comments on an earlier version     

Monotone Games with Positive Spillovers

A monotone game comprises the infinitely repeated play of an n-person stage game, subject to the constraint that players' actions be monotonically nondecreasing over time. These games represent a variety of strategic situations in which players are able to make (partial) commitments. If the stage games have positive spillovers and satisfy certain other conditions, then the limit points of the subgame perfect equilibria are precisely the approachable action profiles. This characterization is applied to voluntary contribution games, market games, and coordination games. Journal of Economic Literature Classification Number: C7.     

Banking,incentive constraints,and demand deposit contracts with nonlinear returns

Summary This paper presents two results regarding banking theory: (1) demand deposit contracts are essential in providing insurance against preferences shocks, as in Diamond and Dybvig (1983), if and only if the incentive compatibility conditions bind at the social optimum; and (2) for additively separable preferences with random discount factors, demand deposit contracts have the realistic feature that the interest rate paid is an increasing function of deposit balance.This paper is based on Chapter 2 of my Ph.D. dissertation submitted to the Graduate School of The University of Minnesota. I am indebted to Neil Wallace for his advice and guidance. I thank an anonymous refree for comments on a previous version of the paper. The comments from Edward Green, Nobuhiro Kiyotaki, Antonio Merlo, and Arijit Mukherji are appreciated.     

Cooperation in an Overlapping Generations Experiment

Recent theoretical work shows that folk theorems can be developed for infinite overlapping generations games. Cooperation in such games can be sustained as a Nash equilibrium. But, of course, there are other equilibria. This paper investigates experimentally whether cooperation actually occurs in a simple overlapping generations game. Subjects both play the game and formulate strategies. Our main finding is that subjects fail to exploit the intertemporal structure of the game. Even when we provided subjects with a recommendation to play the grim trigger strategy, most of the subjects still employed safe history-independent strategies. Journal of Economic Literature Classification Numbers: C72, C92, D90.     

Full revelation of information in Sender-Receiver games of persuasion

We provide necessary and sufficient conditions on both players' preferences and information that can be certified for a Sender-Receiver game to possess a separating equilibrium, as well as sufficient conditions for every equilibrium of such a game to be separating. Accordingly, we generalize Seidmann and Winter's [D.J. Seidmann, E. Winter, Strategic information transmission with verifiable messages, Econometrica 65 (1997) 163-170] results to games with partial provability.     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.