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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 examine the force of three types of behavioral dynamics in quantity-setting triopoly experiments: (1) mimicking the successful firm, (2) rules based on following the exemplary firm, and (3) rules based on belief learning. Theoretically, these three types of rules lead to the competitive, the collusive, and the CournotNash outcome, respectively. In the experiment we employ three information treatments, each of which is hypothesized to be conducive to the force of one of the three dynamic rules. To a large extent, the results are consistent with the hypothesized relationships between treatments, behavioral rules, and outcomes.

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This paper uses laboratory and simulation techniques to examine behavior in two signaling games with different payoff structures. Each game has two sequential equilibria in pure strategies, one of which is ruled out by standard "refinements." The behavior of human subjects approaches the more refined equilibrium in one of the games, but it approaches the less refined equilibrium in the other game. This difference in subjects' decisions is predicted by a simple Bayesian learning process. The period-by-period pattern of adjustment is tracked by computer simulations that incorporate Bayesian learning, logistic decision errors, and some strategic anticipation. Journal of Economic Literature classification: C72, C92 keywords: experiments, game theory, learning, simulations 1. INTRODUCTION The presence of multiple Nash equilibria in all but the simplest games has produced a quest for a Holy Grail that would indicate a unique, plausible outcome in all games. The most common approach has b...

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modeling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f(k). Zero-step players randomize. Players using k ( ≥ 1) steps best respond given partially rational expectations about what players doing 0 through k − 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f(k) has a Poisson distribution (characterized by a mean number of thinking steps τ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1.25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.21) and a median of 1.55 across 60 experimental samples of matrix games, entry games and mixed-equilibrium games. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did. 1

model of learning to extensive-form signaling games. Since these games often have many equilibria, logical ‘refinements ’ have been used to predict which equilibrium will occur. Brandts and Holt conjectured that belief formation could lead to less refined equilibria, and confirmed their conjecture experimentally. Our adaptation of EWA to signaling games includes a formalization of the Brandts-Holt belief formation idea as a special case. We find that the Brandts-Holt dynamic captures the direction of switching from one strategy to another, but does not capture the rate at which switching occurs. EWA does better at predicting the rate of switching (and also forecasts better than reinforcement models). Extensions of EWA which update unchosen signals by different functions of the set of unobserved foregone payoffs further improve predictive accuracy.

We explore how learning to play strategically in one game promotes strategic play in related games. Experiment 1 involves a simple linear transformation in payoffs between games (with presentation format changed as well). There is considerable but incomplete transfer as the growth in the learning process stalls. Experiment 2 changes responders ’ payoffs from supporting a pooling equilibrium to supporting a separating equilibrium. More strategic play is observed following the change than for inexperienced subjects in control sessions, contrary to the prediction of a fictitious play model. We present evidence that experience generates increased numbers of sophisticated players who anticipate responders ’ behavior following the change in payoffs, resulting in positive transfer.

This paper focuses on the process of expectation formation. Specifically, the question is addressed whether individuals think strategically when they form beliefs about other players' behavior. Most belief learning models assume that people abstract from strategic considerations. Using an incentive compatible mechanism, experimental data are o btained on subjects' expectations in a step-level public good game and in a game against nature. Beliefs in the interactive games develop in the same way as in the game against nature, providing evidence that strategic considerations do not play a role. The evidence is consistent with predictions derived from the naive Bayesian model.