Type spaces describe the players beliefs about the other players’ choices, so the notion of an event needs to be relativized to an agent. An event for agent \(i\) is a subset of \(\bigtimes_{j\ne i}T_j\times S\). Again if \(S\) is a set of strategy profiles (so \(S=\bigtimes S_i\)), then an event for agent \(i\) is a subset of \(\bigtimes_{j\ne i} (T_j\times S_j)\).