We use simple learning models to track the behavior observed in experiments concerning three extensive form games with similar perfect equilibria. In only two of the games does observed behavior approach the perfect equilibrium as players gain experience. We examine a family of learning models which possess some of the robust properties of learning noted in the psychology literature. The intermediate term predictions of these models track well the observed behavior in all three games, even though the models considered differ in their very long term predictions. We argue that for predicting observed behavior the intermediate term predictions of dynamic learning models may be even more important than their asymptotic properties.

We describe a general model, `experience-weighted attraction' (EWA) learning, which includes reinforcement learning and a class of weighted fictitious play belief models as special cases. In EWA, strategies have attractions which reflect prior predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter delta which weights the strength of hypothetical reinforcement of strategies which were not chosen according to the payoff they would have yielded. When delta = 0 choice reinforcement results. When delta = 1, levels of reinforcement of strategies are proportional to expected payoffs given beliefs based on past history. Another key feature is the growth rates of attractions. The EWA model controls the growth rates by two decay parameters, phi and rho, which depreciate attractions and amount of experience separately. When phi = rho, belief-based models result; when rho = 0 choice reinforcement results. Using three data se...

‘‘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.

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We combine Nagel’s “step-k” model of boundedly rational players with a “law of effect” learning model. Players begin with a disposition to use one of the step-k rules of behavior, and over time the players learn how the available rules perform and switch to better performing rules. We offer an econometric specification of this dynamic process and fit it to Nagel’s experimental data. We find that the rule of learning model vastly outperforms other nested and nonnested learning models. We find strong evidence for diverse dispositions and reject the Bayesian rule-learning model.

Abstract: We use the experimental method to study people's adaptive behavior in a generic game with multiple Pareto ranked equilibria. The experiment was designed to discover if behavior diverged at the separatrix predicted by the fictitious play dynamic. The equilibrium selected was sensitive to small differences in initial conditions as predicted. The experiment provides some striking examples of coordination failure growing from small historical accidents. Key Words: adaptive learning, fictitious play, path dependence, coordination failure, predictive success. JEL classification: c720, c920. Acknowledgments: Artie Powell made valuable comments on the experimental design and helped run the experiments reported in this paper. The power of the equilibrium method derives from the ability to abstract from the dynamic process that produces mutually consistent

Coordination games with Pareto-ranked equilibria have attracted major attention over the past two decades. Two early path-breaking sets of experimental studies were widely interpreted as suggesting that coordination failure is a common phenomenon in the laboratory. We identify the major determinants that seem to affect the incidence, and/or emergence, of coordination failure in 1 the lab and review critically the existing experimental studies on coordination games with Paretoranked equilibria since that early evidence emerged. We conclude that there are many ways to engineer coordination successes. 1.

Abstract. This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria, nor do they alter the predictions of dynamic adjustment theories based on imitation or best responses to others ’ decisions. As would be expected, however, increases in effort cost result in reduced effort levels. Average behavior in the final periods is consistent with a one-parameter stochastic generalization of the Nash equilibrium that is calculated by maximizing a "stochastic potential function. " The noise parameter estimated from the initial twoperson, minimum-effort games is used to predict behavior in subsequent experiments with threeperson games, using both minimum and medium-effort payoff structures. JEL Classification: C72, C92.

Previous studies have shown that simply knowing one player moves first can affect behavior in games, even when the first-mover’s moves are known to be unobservable. This observation violates the game-theoretic principle that timing of unobserved moves is irrelevant, but is consistent with virtual observability, a theory of how timing can matter without the ability to observe actions. However, this previous research only shows that timing matters in games where knowledge that one player moved first can help select that player’s preferred equilibrium, presenting an alternative explanation to virtual observability. We extend this work by varying timing of unobservable moves in ultimatum bargaining games and “weak link ” coordination games. In the latter, the equilibrium selection explanation does not predict any change in behavior due to timing differences. We find that timing without observability affects behavior in both games, but not substantially. 1 I.

This paper revisits the minimum-effort coordination game with a continuum of Paretoranked Nash equilibria. Noise is introduced via a logit probabilistic choice function. The resulting logit equilibrium distribution of decisions is unique and maximizes a stochastic potential function. In the limit as the noise vanishes, the distribution converges to an outcome that is analogous to the risk-dominant outcome for 22 games. In accordance with experimental evidence, logit equilibrium efforts decrease with increases in effort costs and the number of players, even though these parameters do not affect the Nash equilibria.