 If \(\boldsymbol{\mu}^*\) is a strict equilibrium, then one can predict which pure strategy profile the agents in a game will follow given common knowledge of the game, rationality and \(\boldsymbol{\mu}^*.\) But if \(\boldsymbol{\mu}^*\) is such that several distinct pure strategy profiles satisfy (3.iv) with respect to \(\boldsymbol{\mu}^*\), then one can no longer predict with certainty what the agents will do. For instance, in the Chicken game of Figure 3.1, the belief distributions defined by \(\alpha_1 = \alpha_2 = 2/3\) together are a Nash equilibrium-in-beliefs. Given common knowledge of this equilibrium, either pure strategy is a best reply for each agent, in the sense that either pure strategy maximizes expected utility. Indeed, if agents can also adopt randomized or mixed strategies at which they follow one of several pure strategies according to the outcome of a chance experiment, then any of the infinitely mixed strategies an agent might adopt in Chicken is a best reply given  \(\boldsymbol{\mu}^*\).[25]  So the endogenous correlated equilibrium concept does not determine the exact outcome of a game in all cases, even if one assumes probabilistic consistency and independence so that the equilibrium is a Nash equilibrium.