Games and Economic Behavior 51 (2005) 296–323 www.elsevier.com/locate/geb Random belief equilibrium in normal form games James W. Friedman ∗ , Claudio Mezzetti Department of Economics, CB #3305, University of North Carolina, Chapel Hill, NC 27599-3305, USA Received 4 May 2001 Available online 6 November 2003 Abstract In defining random belief equilibrium (RBE) in finite, normal form games we assume a player’s beliefs about others’ strategy choices are randomly drawn from a belief distribution that is dispersed around a central strategy profile, the focus. At an RBE: (1) Each chooses a best response relative to her beliefs. (2) Each player’s expected choice 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 also characterize the limit-RBE as players’ beliefs converge to certainty. When atoms in the belief distributions vanish in the limit, not all limit-RBE (called robust equilibria) are trembling hand perfect Nash equilibria and not all perfect equilibria are robust.  2003 Elsevier Inc. All rights reserved. JEL classification: C44; C72; C92 Keywords: Random belief equilibrium; Quantal response equilibrium; Nash equilibrium; Normal form games; strategic form games 1. Introduction Equilibrium concepts typically include, either implicitly or explicitly, beliefs that play- ers have about how rival players will play. For Nash equilibrium these beliefs must be exactly correct; that is, they must put all probability mass on the precise equilibrium strate- gies followed by others. On the other hand, rationalizability, due to Bernheim (1984) and * Corresponding author. E-mail addresses: jim_friedman@unc.edu (J.W. Friedman), mezzetti@email.unc.edu (C. Mezzetti). 0899-8256/$ – see front matter  2003 Elsevier Inc. All rights reserved. doi:10.1016/j.geb.2003.08.004