A Centipede Game In the centipede game, the two players move alternatingly. On each move, a player can stop (S) or continue (C). On any move, a player is better off stopping the game than continuing...

A Centipede Game

In the centipede game, the two players move alternatingly. On each move, a player can stop (S) or continue (C). On any move, a player is better off stopping the game than continuing if the other player stops immediately afterward, but is worse off stopping than continuing if the other player continues, regardless of the subsequent actions. The game ends after a finite number of periods. Consider an example of this game in Fig. 4.15.

(a) Determine the backward induction or subgame perfect equilibrium of this game. What is the associated outcome?

(b) Show that there are other Nash equilibria, but that these always result in the same outcome as the subgame perfect equilibrium.

Fig. 4.15