The centipede game The centipede game has four stages (see Figure 10.5). At each stage, a player can Take, thereby ending the game, or Pass, thereby increasing the total payoff and allowing the other player to move.

(a) Use backward induction to find the unique subgame-perfect equilibrium.

(b) Would the outcome of the game differ if it had 1000 stages instead of four? I II I II (1,0) (0,2) Figure 10.5 The centipede game (3,0) (0,4) (5,0)