We define Random Belief Equilibrium (RBE) in finite, normal form games. We assume that a player's beliefs about the strategy choices of others are randomly drawn from a belief distribution. This distribution is dispersed around a central strategy profile, the focus. At an RBE: (1) Each player chooses a best response relative to her drawn beliefs. (2) The expected choice of each player coincides with the focus of the other players' belief distributions. We provide a characterization of the limiting RBE as players' beliefs converge to certainty. The limiting RBE is a trembling hand perfect Nash equilibrium, but not all perfect equilibria are limiting RBE. Being a limiting RBE is neither necessary nor sufficient for being weakly proper. Using maximum likelihood estimation, we find that RBE fits the data from several experimental games significantly better than the Quantal Response Equilibrium of McKelvey and Palfrey.

Co-author James W. Friedman