Vertigo: Comparing Structural Models of Imperfect Behavior in Experimental Games

Abstract

This paper investigates learning in games with one-sided incomplete information using laboratory data from a game which we call the game of Vertigo. The predicted Bayes-Nash equilibrium behavior of the agents in this type of game generates overly strong restrictions on the data, including the zero likelihood problem: certain actions should never be observed. To circumvent statistical problems, and to allow for deviations from perfectly rational behavior, we introduce the possibility of players making errors when choosing their actions. We compare two competing models depending on whether players take the errors in actions into consideration when formulating their strategies. We also investigate possible deviations from Bayes's rule, producing too fast or too slow an updating rule. In total, we get six models of sophisticated and unsophisticated strategy formation on the first dimension, and fast, slow, or no updating on the second. We apply a fully Bayesian structural econometric approach to compare the statistical performance of these six models, and to obtain posterior estimates of several nuisance parameters governing the errors in actions. The two models where players are unsophisticated and either use no updating at all, or use dampened updating, have a much higher likelihood than any of the others.