Consider a variant of the game in Exercise 1, in which the player who moves the rock into cell (1, 1) wins the game.
(a) Does one of the players have a strategy that guarantees him a win? If so, which player has a winning strategy?
(b) Now consider a three-player version of the game, whereby play rotates between the 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.
Players are allowed to move the rock just as described above. The player who moves the rock into cell (1, 1) wins and gets a payoff of 1; the other two players lose, each obtaining 0. Is there a subgame perfect equilibrium in which player 1 wins?
Is there a subgame perfect equilibrium in which player 2 wins? Is there a subgame perfect equilibrium in which player 3 wins?