Centipedes Revisited: Two players are playing two consecutive games. First, they play the Centipede Game described in Figure 2. After the Centipede Game they play the following coordination game:
a. What are the Nash equilibria of each stage-game?
b. How many pure strategies does each player have in the multistage game?
c. Find all the pure-strategy subgame-perfect equilibria with extreme discounting (δ = 0). Be precise in defining history-contingent strategies for both players.
d. Now let δ = 1. Find a subgame-perfect equilibrium for the two-stage game in which the players receive the payoffs (2, 2) in the first stagegame.
e. What is the lowest value of δ for which the subgame-perfect equilibrium you found in (d) survives? f. For δ greater than the value you found in (e), are there other outcomes of the first-stage Centipede Game that can be supported as part of a subgame-perfect equilibrium?
