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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...

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This paper reports an experiment that elicits subjects ’ initial responses to 16 dominance-solvable two-person guessing games. The structure is publicly announced except for varying payoff parameters, to which subjects are given free access. Varying the parameters allows very strong separation of the behavior implied by leading decision rules. Subjects ’ decisions and searches show that most subjects understood the games and sought to maximize payoffs, but many had simplified models of others ’ decisions that led to systematic deviations from equilibrium. The predictable component of their deviations is well explained by a structural nonequilibrium model of initial responses based on level-k thinking. (JEL C72, C92, D83)... professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth, and higher degrees.

We review the current state of the art of methods for numerical computation of Nash equilibria for niten-person games. Classical path following methods, such as the Lemke-Howson algorithm for two person games, and Scarf-type fixed point algorithms for n-person games provide globally convergent methods for finding a sample equilibrium. For large problems, methods which are not globally convergent, such as sequential linear complementarity methods may be preferred on the grounds of speed. None of these methods are capable of characterizing the entire set of Nash equilibria. More computationally intensive methods, which derive from the theory of semi-algebraic sets are required for finding all equilibria. These methods can also be applied to compute various equilibrium refinements.

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.

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Players in a game are “in equilibrium ” if they are rational, and accurately predict other players ’ strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy ” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k � 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games. I.

Behavioral economics increases the explanatory power of economics by providing it with more realistic psychological foundations. This book consists of representative recent articles in behavioral economics. This chapter is intended to provide an introduction to the approach and methods of behavioral economics, and to some of its major findings, applications, and promising new directions. It also seeks to fill some unavoidable gaps in the chapters’ coverage of topics.