Beyond Fictitious Play Beliefs: Incorporating Pattern Recognition and Similarity Matching

Abstract

Belief models capable of detecting 2- to 5-period patterns in repeated games by matching the current historical context to similar realizations of past play are presented. The models are implemented in a cognitive framework, ACT-R, and vary in how they implement similarity-based categorization — using either an exemplar or a prototype approach. Empirical estimation is performed on the elicited-belief data from two experiments (Nyarko and Schotter, 2002; Rutström and Wilcox, 2009) using repeated games with a unique, albeit significantly different, stage mixed-strategy Nash equilibrium. Model comparisons are performed by cross-validation both within and between these two datasets, and using data from completely unrelated non-strategic tasks. Subjects’ beliefs are best described by 2-period pattern detection. Parameter estimates exhibited considerable instability across the two belief-elicitation datasets, and surprisingly, using median values from a wide variety of unrelated studies led to better predictions.

Keywords: Learning, Pattern recognition, Beliefs, Repeated games, Memory, Cognitive models, Behavioral game theory, ACT-R

JEL Classification: C70, C72, C73, C91, C52, C53