Consider again the running example of the coordination game between Ann and Bob (pictured in Figure 1). In this case, the set of states of nature is \(S=\{(u,l),(d,l),(u,r),(d,r)\}\). In this context, it is natural to modify the definition of the type functions \(\lambda_i\) to account for the fact that the players are only uncertain about the other players’ choices: let \(S_A=\{u,d\}\) and \(S_B=\{l,r\}\) and suppose \(T_A\) and \(T_B\) are nonempty sets of types. Define \(\lambda_A\) and \(\lambda_B\) as follows: