We test whether a model of reputation formation in an incomplete information game, using sequential equilibrium, predicts behavior of players in an experiment. Subjects play an abstracted lending game: a B player lends or does not lend; then if B lends, an E player can pay back or renege. The game is played 8 times, and there is a small controlled probability that the E player's induced preferences make him prefer to pay back (but usually he prefers to renege). In sequential equilibrium, even E players who prefer to renege should pay back in early periods of the game, and renege with increasing frequency in later periods, to establish reputations for preferring to pay back. After many repetitions of the 8-period game, actual play is roughly like the sequential equilibrium, except that E players pay back later in the game and more often than they should. This behavior is rational if B players have a "homemade" prior probability of .17 (in addition to the controlled probability) that E players will prefer to pay back. We conclude that sequential equilibrium with homemade incomplete information describes actual behavior well enough that it is plausible to apply it to theoretical settings where individuals make choices (e.g., product markets, labor markets, bargaining).

In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do.

Many alternative theories have been proposed to explain violations of expected utility (EU) theory observed in experiments. Several recent studies test some of these alternative theories against each other. Formal tests used to judge the theories usually count the number of responses consistent with the theory, ignoring systematic variation in responses that are inconsistent. We develop a maximum-likelihood estimation method which uses all the information in the data, creates test statistics that can be aggregated across studies, and enables one to judge the predictive utility-the fit and parsimony-of utility theories. Analyses of 23 data sets, using several thousand choices, suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit. The menu is: mixed fanning, prospect theory, EU, and expected value. Which theories are best is highly sensitive to whether gambles in a pair have the same support (EU fits better) or not (EU fits poorly). Our method may have application to other domains in which various theories predict different subsets of choices (e.g., refinements of Nash equilibrium in noncooperative games).