Division of the Humanities and Social Sciences California Institute of Technology Pasadena, California 91125 Experience-weighted Attraction Learning in Normal Form Games

We describe a general model, `experience-weighted attraction' (EWA) learning, which includes reinforcement learning and a class of weighted ctitious play belief models as special cases. In EWA, strategies have attractions which re ect prior predispositions, are updated based on payo experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter which weights the strength of hypothetical reinforcement of strategies which were not chosen according to the payo they would have yielded. When = 0 choice reinforcement results. When = 1, levels of reinforcement of strategies are proportional to expected payo s 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, and , which depreciate attractions and amount of experience separately. When = , belief-based models result; when = 0 choice reinforcement results. Using three data sets, parameter estimates of the model were calibrated on part of the data and used to predict the rest. Estimates of are generally around .50, around 1, and varies from 0 to . Choice reinforcement models often outperform belief-based models in the calibration phase and underperform in out-of-sample validation. Both special cases are generally rejected in favor of EWA, though sometimes belief models do better. EWA is able to combine the best features of both approaches, allowing attractions to begin and grow exibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do.