 One might propose that both players should choose that strategy which maximizes their expected payoff on the assumption they are uncertain as to whether they will be assigned the role of Player 1 or Player 2. This proposal, Skyrms notes, is essentially that of Harsanyi (1953). The problem with this is that if players only care about their expected payoff, and they think that it is equally likely that they will be assigned the role of Player 1 or Player 2, then this, too, fails to select uniquely the equal split. Consider the strategy profile \(\langle p, C - p\rangle\) which assigns Player 1 \(p\) slices and Player 2 \(C - p\) slices. If a player thinks it is equally likely that he will be assigned the role of Player 1 or Player 2, then his expected utility is \(\frac{1}{2} p + \frac{1}{2}(C - p) = \frac{C}{2}\), for all values \(p \in[0, C]\).