 We have a clear intuition that the “obvious” strategy for each player to select is C/2; the philosophical problem lies in explaining why agents would choose that strategy rather than some other one. Even in the perfectly symmetric situation, answering this question is more difficult than it first appears. To see this, first notice that there are an infinite number of Nash equilibria for this game. If player 1 asks for \(p\) of the cake, where \(0 \le p \le C\), and player 2 asks for \(C - p\), then this strategy profile is a Nash equilibrium for any value of \(p \in [0,C]\). (Each player’s strategy is a best response given what the other has chosen, in the sense that neither player can increase her payoff by changing her strategy.) Thus the equal split is only one of infinitely many Nash equilibria.