Consider a three-player version of Chomp. Play rotates between the three players, starting with player 1. That is, player 1 moves first, followed by player 2, then player 3, then back to player 1, and so on. The player who is forced to select cell (1, 1) loses the game and gets a payoff of 0. The player who moved immediately before the losing player obtains 1, whereas
the other player wins with a payoff of 2.

(a) Does this game have a subgame perfect Nash equilibrium?

(b) Do you think any one of the players has a strategy that guarantees him a win (a payoff of 2)?

(c) Can you prove that player 1 can guarantee himself any particular payoff? Sketch your idea.