NAIVE BAYESIAN LEARNING IN 2X2 MATRIX GAMES

This paper looks at sequences of two-player games where each player 'naively' assumes that his opponent follows a certain mixed strategy which can be learned by observing his behaviour. In each stage of the game players up-date their beliefs and choose an optimal response to the expected behaviour of the opponent. Provided that this learning process converges, the equilibrium beliefs form a Nash equilibrium. Hence, it is possible to derive a probability distribution on the set of Nash equilibria conditional on the players' prior beliefs. For prior distributions of the beta-distribution type, it can be shown that the learning process converges. Some examples illustrate how this fact can be used in games with multiple equilibria to obtain a probability distribution on the equilibrium set.