Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach

This paper proposes an equilibrium concept for n-person finite games based on boundedly rational decision making by players. The players are modeled as following random choice behavior in the manner of the logit model of discrete choice theory as set forth by Luce, McFadden and others. The behavior of other players determines in a natural way a lottery facing each player i. At equilibrium, each player is using the appropriate choice probabilities, given the choice probabilities used by the others in the game. The rationality of the players is parameterized on a continuum from complete rationality to uniform random choice. Using results by McKelvey and Palfrey, we show existence of an equilibrium for any finite n-person game and convergence to Nash equilibrium. We also identify conditions such that, for given rationality parameters the path of choices over time when the players use fictitious play (their beliefs about other players' choices are given by the empirical distributions of those players) converges to equilibrium.