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. RBE provides a statistical framework for estimation which we apply to data from three experimental games.

We provide a characterization of the limit-RBE as players' beliefs converge to certainty. Let D_i ( s_i ) be he set of mixed strategies of player i's opponents to which s_i is a best reply. When atoms in the belief distributions vanish in the limit, all pure strategies s_i used with positive probability by player i in a limit-RBE (called a Robust Equilibrium) must have the following property. The intersection of D_i ( s_i ) with any ball around the equilibrium mixed strategies of player i's opponents must have positive Lebesgue measure. We show that this implies that not all trembling hand perfect Nash equilibria are robust and not all robust equilibria are perfect.

Keywords: random belief equilibrium, quantal response equilibrium, Nash equilibrium, normal form games, strategic form games.
 
Journal of Economic Literature Classification Numbers: C44, C72, C92.