 so each agent maximizes her expected utility by playing \(s_1\) if \(\alpha_i + 2 \ge 4\alpha_i\) or \(\alpha_i \le 2/3\) and maximizes her expected utility by playing \(s_2\) if \(\alpha_i \ge 2/3\). If it so happens that \(\alpha_i \gt 2/3\) for both agents, then both conform with Bayesian rationality by playing their respective ends of the strategy combination \((s_2,s_2)\) given their beliefs, even though each would want to defect from this strategy combination were she to discover that the other is in fact going to play \(s_2\). Note that the game’s pure strategy Nash equilibria, \((s_1, s_2)\) and \((s_2, s_1)\), are rationalizable, since it is rational for Lizzi and Joanna to conform with either equilibrium given appropriate distributions. In general, the set of a game’s rationalizable strategy combinations contains the set of the game’s pure strategy Nash  equilibria.[23]