Pattern recognition and subjective belief learning in repeated mixed strategy games

This paper aspires to fill a conspicuous gap in the existing literature on learning in games, namely the absence of any empirical verification of learning rules involving pattern recognition. An extension of weighted fictitious play is proposed both obeying cognitive laws of subjective perception, and allowing for two-period pattern detection of opponents' behavior. The unconditional prior probability of a subject employing a pattern detecting belief model is 0.34, as estimated by a mixture (latent-class) model of the elicited belief and action data series from Nyarko and Schotter (2002), or 0.551 using only action data. The conditional prior probability of using pattern recognition was found to depend positively on a measure of the exploitable two-period patterns in an opponent's action choices, in stark contrast to the minimax hypothesis. Also, standard weighted fictitious play models are found to significantly bias memory parameter estimates upwards, compared to the proposed subjective fictitious play models. Finally, simulations of learning models reveal that the simple win-stay/lose-shift heuristic may be effective even against more complex pattern detecting models.