 Proposition 3.12 says that far less than common knowledge of the game and of rationality suffices for the backwards induction solution to obtain in a game of perfect information. All that is needed is for each agent at each of her information sets to be rational, to know the game and to know what the next agent to move knows! For instance, in the Figure 1.2 game, if \(R_1 (R_2)\) stands for “Alan (Fiona) is rational” and \(\mathbf{K}_i (\Gamma)\) stands for “\(i\) knows the game \(\Gamma\)”, then the backwards induction solution is implied by the following: