One of the simplest approaches is to use the epistemic models introduced in Section 2.2 (cf.  Aumann 1995; Halpern 2001b). An epistemic model of an extensive game \(G=\langle N, T, Act, \tau, \{ u_i \}_{i \in N}\rangle\) is a tuple \(\langle W, \{\Pi_i\}_{i\in N}, \sigma\rangle \) where \(W\) is a nonempty set of states; for each \(i\in N\), \(\Pi_i\) is a partition on \(W\); and \(\sigma:W\rightarrow \Pi_{i\in N} S_i\) is a function assigning to each state \(w\), a strategy profile from \(G\). If \(\sigma(w)={\mathbf{s}}\), then we write \(\sigma_i(w)\) for \({\mathbf{s}}_i\) and \(\sigma_{-i}(w)\) for \({\mathbf{s}}_{-i}\). As usual, we assume that players know their own strategies: for all \(w\in W\), if \(w'\in \Pi_i(w)\), then \(\sigma_i(w)=\sigma_i(w')\).