 If \(\boldsymbol{\mu}^*\) is an endogenous correlated equilibrium a pure strategy combination \(\boldsymbol{s}^* = (s_1^*, \ldots ,s_n^*) \in S\) is an endogenous correlated equilibrium strategy combination given \(\boldsymbol{\mu}^*\) if, and only if, for each agent \(k \in N,\)