 As this example illustrates, there are several legitimate ways of comparing games. When taking a fine-grained focus on the internal structure of a game, a natural candidate is the notion of a bisimulation (cf. Blackburn, de Rijke, &amp; Venema 2001). A bisimulation \(Z\subseteq G_1\times G_2\) relates states of two game forms \(G_1\) and \(G_2\) subject to four conditions: States m and n may only be related when (i) the same player is to move in m and n, (ii) m and n do not differ in any of their basic local properties, while (iiia) whenever there is an available move of type a in \(G_1\) leading to a state \(m'\), there is a matching available move of type a in \(G_2\) leading to a state \(n'\) with \(m'Zn'\), and vice versa (iiib) whenever there is a move in \(G_2\) that leads to a state \(n'\), there there is a move of the same type in \(G_1\) leading to a state \(m'\) with \(m'Zn'\).