 Definition 3.3. Given any pair of games \(G,H\), the game \(G \multimap H\) has moves \(M_{G \multimap H}\) the disjoint union \(M_G + M_H\) of the games \(G\) and \(H\), where   \[\lambda_{G \multimap H} (m) =   \begin{cases}          \overline{\lambda_{G}} (m) =   &amp;\text{if \(m \in M_G\),}\\     \lambda_{H} (m) =   &amp;\text{if \(m \in M_H\).}     \end{cases}\]  and a position in \(P_{G \multimap H}\) is any alternating sequence \(s\) of moves (of \(M_{G \multimap H}\)) whose restrictions \(s \upharpoonright M_G,s \upharpoonright M_H\) to the moves in \(G\) and \(H\), respectively, are positions of \(G\) and \(H\).