Definition 4.5 (Rationality at a decision node) Player \(i\) is rational at node \(v\in V_i\) in state \(w\) provided, for all strategies \(s_i\) such that \(s_i\ne \sigma_i(w)\), there is an \(o'\in Out_i(v, s_i, S_{-i}(w))\) and \(o\in Out_i(v, \sigma_i(w), S_{-i}(w))\) such that \(u_i(o)\ge u_i(o')\).