Empirical properties and identification of adaptive learning models in behavioral game theory

Abstract

This paper studies the empirical properties and identification for a broad class of adaptive learning models in games (e.g., experience-weighted attraction (EWA), payoff assessment, and impulse-matching models). I first show that adding a constant c≠0 to the utility function could affect players’ choices during the learning periods. This property is different from standard theories, such as expected utility theory and discrete choice models, where adding c≠0 preserves the same choice. This result has two further implications. First, the constant c added to the utility function could have a structural interpretation, and this paper discusses how to interpret it. Second, the estimation of learning models usually normalizes the utility of one action profile to be zero (i.e., c=0); for instance, the utility of zero dollars is zero, as commonly imposed in experimental economics. This normalization is innocuous in most applications of discrete choice models but could be misspecified in the context of learning. To deal with the above issue, this paper proposes to specify a player’s utility as an unknown function of the action profile, without imposing the above normalization. Equivalently, c is specified as an unknown parameter to be estimated. Under weak conditions, I obtain the joint identification of both utility and learning parameters. Finally, I illustrate the importance of c in the estimation of learning models by conducting a Monte Carlo experiment and revisiting the experimental study by Feri et al. (2010).