We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimatation.

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Reinforcement learning can provide a robust and natural means for agents to learn how to coordinate their action choices in multiagent systems. We examine some of the factors that can influence the dynamics of the learning process in such a setting. We first distinguish reinforcement learners that are unaware of (or ignore) the presence of other agents from those that explicitly attempt to learn the value of joint actions and the strategies of their counterparts. We study (a simple form of) Q-learning in cooperative multiagent systems under these two perspectives, focusing on the influence of that game structure and exploration strategies on convergence to (optimal and suboptimal) Nash equilibria. We then propose alternative optimistic exploration strategies that increase the likelihood of convergence to an optimal equilibrium.

Abstract Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique, dominance solvable equilibrium, allowing analysis of a number of economic models of coordination failure. For symmetric binary action global games, equilibrium strategies in the limit (as noise becomes negligible) are simple to characterize in terms of 'diffuse' beliefs over the actions of others. We describe a number of economic applications that fall in this category. We also explore the distinctive roles of public and private information in this setting, review results for general global games, discuss the relationship between global games and a literature on higher order beliefs in game theory * This paper was prepared for the Eighth World Congress of the Econometric Society (Seattle 2000). Section 3 incorporates work circulated earlier under the title "Private versus Public Information in Coordination Problems." We would like to thank Hans Carlsson, David Frankel, Josef Hofbauer, Jonathan Levin and Ady Pauzner for valuable comments on the paper, and Susan Athey for her insightful remarks as discussant at the Congress. Morris would like to record an important intellectual debt in this area to Atsushi Kajii, through joint research and long discussions. Morris is grateful for financial support from National Science Foundation grant #9709601. and describe the relationship to local interaction games and dynamic games with payoff shocks.

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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others’ decisions.

We extend Q-learning to a noncooperative multiagent context, using the framework of generalsum stochastic games. A learning agent maintains Q-functions over joint actions, and performs updates based on assuming Nash equilibrium behavior over the current Q-values. This learning protocol provably converges given certain restrictions on the stage games (defined by Q-values) that arise during learning. Experiments with a pair of two-player grid games suggest that such restrictions on the game structure are not necessarily required. Stage games encountered during learning in both grid environments violate the conditions. However, learning consistently converges in the first grid game, which has a unique equilibrium Q-function, but sometimes fails to converge in the second, which has three different equilibrium Q-functions. In a comparison of offline learning performance in both games, we find agents are more likely to reach a joint optimal path with Nash Q-learning than with a single-agent Q-learning method. When at least one agent adopts Nash Q-learning, the performance of both agents is better than using single-agent Q-learning. We have also implemented an online version of Nash Q-learning that balances exploration with exploitation, yielding improved performance.

We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (1993) for two player, two action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.

‘‘Human experience, which is constantly contradicting theory, is the great test of truth.’’ �Dr. Johnson, quoted in James Boswell, The Life of Samuel Johnson L.L.D. This paper reports experiments designed to study strategic sophistication, the extent to which behavior in games reflects attempts to predict others ’ decisions, taking their incentives into account. We study subjects ’ initial responses to normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer interface that allowed them to search for hidden payoff information, while recording their searches. Monitoring subjects ’ information searches along with their decisions allows us to better understand how their decisions are determined, and subjects ’ deviations from the search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.