  Critics such as John Nachbar (1997) and Dean Foster and H. Peyton Young (2001) argue that there is no reason to accept the “grain of truth” assumption. From this perspective, Kalai and Lehrer merely push the problem back to explaining how players converge upon a suitable set of prior probabilities satisfying the “grain of truth” assumption. Although Kalai and Lehrer’s proof actually requires only a somewhat weakened version of this assumption, the problem persists: sophisticated Bayesian learning converges to Nash equilibrium only under special assumptions about players’ prior coordinated expectations, assumptions that players might well fail to satisfy.