 Suppose that \(G=\langle N, \{S_i, u_i\}_{i\in N}\rangle\) is a strategic game. A conjecture for player \(i\) is a probability on the set \(S_{-i}\) of strategy profiles of \(i\)’s opponents. That is, a conjecture for player \(i\) is an element of \(\Delta(S_{-i})\), the set of probability measures over \(S_{-i}\). The expected utility of \(s_i\in S_i\) with respect to a conjecture \(p\in \Delta(S_{-i})\) is defined as follows: