A Probabilistic Model of Learning in Games

Abstract

This paper presents a new, probabilistic model of learning in games which investigates the often stated intuition that common knowledge of strategic intent may arise from repeated interaction. The model is set in the usual repeated game framework, but the two key assumptions are framed in terms of the likelihood of beliefs and actions conditional on the history of play. The first assumption formalizes the basic intuition of the learning approach; the second, the indeterminacy that inspired resort to learning models in the first place. Together the assumptions imply that, almost surely, play will remain almost always within one of the stage game's minimal inclusive sets. In important classes of games, including those with strategic complementarities, potential functions, and bandwagon effects, all such sets are singleton Nash.