 Definition 3.1 A game \(G\) is specified by giving a set of moves \(M_G\), a labeling \(\ell_G\) of the moves as either moves of the Proponent (\(P\)) or as moves of the Opponent (\(O\)). Furthermore, there is a set of positions \(P_G\) which is a set of sequences of moves where: (1) the two players alternate, starting with \(O\); (2) if \(s \in P_G\) then every prefix \(s'\) of \(s\) is also in \(P_G\).