24.2 Consider a sequential game that is known as the Centipede Game. In this game, each of two players chooses between Left and Right each time he or she gets a turn. The game does not, however, automatically proceed to the next stage unless players choose to go Right rather than Left.

A. Player 1 begins, and if he plays Left, the game ends with payoff of (1,0) (where here, and throughout this exercise, the first payoff refers to player 1 and the second to player 2). If, however, he plays Right, the game continues and it’s player 2’s turn. If player 2 then plays Left, the game once again ends, this time with payoffs (0,2), but if she plays Right, the game continues and player 1 gets another turn. Once again, the game ends if player 1 decides to play Left, this time with payoffs of (3,1), but if he plays Right the game continues and it’s once again player 2’s turn. Now the game ends regardless of whether player 2 plays Left or Right, but payoffs are (2,4) if she plays Left and (3,3) if she plays Right.