 Like the Farmers’ Dilemma, this game is a commitment problem for the agents. If each agent could trust the other to choose \(R^i\) at each stage, then they would each expect to receive a payoff of 3. However, Alan chooses \(L^1\), leaving each with a payoff of only 1, as the result of the following backwards induction argument: “If node \(n_4\) were to be reached, then Fiona, (being rational) would choose \(L^4\). I, knowing this, would (being rational) choose \(L^3\) if node \(n_3\) were to be reached. Fiona, knowing this, would (being rational) choose \(L^2\) if node \(n_2\) were to be reached. Hence, I (being rational) should choose \(L^1\).” To carry out this backwards induction argument, Alan implicitly assumes that: (i) he knows that Fiona knows he is rational, and (ii) he knows that Fiona knows that he knows she is rational. Put another way, for Alan to carry out the backwards induction argument, at node \(n_1\) he must know what Fiona must know at node \(n_2\) to make \(L^2\) her best response should \(n_2\) be reached. While in the Farmer’s Dilemma Fiona needed only first-order knowledge of Alan’s rationality and second-order knowledge of Alan’s knowledge of the game to derive the backwards induction solution, in the Figure 1.2 game, for Alan to be able to derive the backwards induction solution, the agents must have third-order mutual knowledge of the game and second-order mutual knowledge of rationality, and Alan must have fourth-order knowledge of this mutual knowledge of the game and third-order knowledge of their mutual knowledge of rationality. This argument also involves several counterfactuals, since to construct it the agents must be able to evaluate conditionals of the form, “If node \(n_i\) were to be reached, Alan (Fiona) would choose \(L^i (R^i)\)”, which for \(i \gt 1\) are counterfactual, since third-order mutual knowledge of rationality implies that nodes \(n_2,\) \(n_3\), and \(n_4\) are never reached.