Each strategy profile \({\mathbf{s}}\) generates a path through an extensive game, where a path is a maximal sequence of nodes from the extensive game ordered by the immediate successor relations \(\rightarrowtail\). We say that \(v\) is reached by a strategy profile \({\mathbf{s}}\) is \(v\) is on the path generated by \({\mathbf{s}}\). Suppose that \(v\) is any node in an extensive game. Let \(out(v,{\mathbf{s}})\) be the terminal node that is reached if, starting at node \(v\), all the players move according to their respective strategies in the profile \({\mathbf{s}}\). Given a decision node \(v\in V_i\) for player \(i\), a strategy \(s_i\) for player \(i\), and a set \(X\subseteq S_{-i}\) of strategy profiles of the opponents of \(i\), let \(Out_i(v,s_i, X)=\{out(v, (s_i, s_{-i})) \mid s_{-i}\in X\}\). That is, \(Out_i(v, s_i, X)\) is the set of terminal nodes that may be reached if, starting at node \(v\), player \(i\) uses strategy \(s_i\) and \(i\)’s opponents use strategy profiles from \(X\).