Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment

The purpose of this paper is to reexamine the seminal belief elicitation experiment by Nyarko and Schotter (2002) under the prism of pattern recognition. Instead of modeling elicited beliefs by a standard weighted fictitious play model this paper proposes a generalized variant of fictitious play that is able to detect two period patterns in opponents’ behavior. Evidence is presented that these generalized pattern detection models provide a better fit than standard weighted fictitious play. Individual heterogeneity was discovered as ten players were classified as employing a two period pattern detection fictitious play model, compared to eleven players who followed a non-pattern detecting fictitious play model. The average estimates of the memory parameter for these classes were 0.678 and 0.456 respectively, with five individual cases where the memory parameter was equal to zero. This is in sharp contrast to the estimates obtained from standard weighted fictitious play models which are centred on one, a bias introduced by the absence of a constant in these models. Non-pattern detecting fictitious play models with memory parameters of zero are equivalent to the win-stay/lose-shift heuristic, and therefore some sub jects seem to be employing a simple heuristic alternative to more complex learning models. Simulations of these various belief formation models show that that this simple heuristic is quite effective against other more complex fictitious play models.