Pattern Recognition and Subjective Belief Learning in a Repeated Constant-Sum Game

Abstract

This paper aspires to fill a conspicuous gap in the literature regarding learning in games — the absence of empirical verification of learning rules involving pattern recognition. Weighted fictitious play is extended to detect two-period patterns in opponents’ behavior and to comply with the cognitive laws of subjective perception. An analysis of the data from Nyarko and Schotter (2002) uncovers significant evidence of pattern recognition in elicited beliefs and action choices. The probability that subjects employ pattern recognition depends positively on a measure of the exploitable two-period patterns in an opponent’s action choices, in stark contrast to the minimax hypothesis. A significant proportion of the subjects’ competence in pattern recognition is the result of a subconscious/automatic cognitive mechanism, implying that elicited beliefs may not adequately represent the complete learning process of game players. Additionally, standard weighted fictitious play models are found to bias memory parameter estimates upwards due to mis-specification.

Keywords: Behavioral game theory, Learning, Fictitious play beliefs, Pattern detection, Repeated constant-sum games

JEL Classification: C91, C70, C72, C73