9.2 Centipedes Revisited: Two players are playing two consecutive games. First,
ID: 1107891 • Letter: 9
Question
9.2 Centipedes Revisited: Two players are playing two consecutive games. First, they play the Centipede Game described in Figure 9.2. After the Centipede Game they play the following coordination game: Player 2 A110,0 B 0,0 3,3 Player 1 What are the Nash equilibria of each stage-game? game? counting (8-0). Be precise in defining history-contingent strategies a. b. How . Find all the pure-strategy subgame-perfect equilibria with extreme dis- d. Now let -1. Find a subgame-perfect equilibrium for the two-stage e, what is the lowest value of for which the subgame-perfect equilib- f. For greater than the value you found in (c), are there other outcomes many pure strategies does each player have in the multistage for both players. game in which the players receive the payoffs (2, 2) in the first stage- game. rium you found in (d) survives? of the first-stage Centipede Game that can be supported as part of a subgame-perfect equilibrium?Explanation / Answer
A) The rst stage game has a unique Nash equilibrium outcome in which player 1 plays N in the rst stage and payos are (1,1). This can be supported in more than oneNash equilibrium (for example, player 1 plays N always and player 2 plays n always,which is the subgame perfect equilibrium, or player 1 player N always and player2 plays n rst and c later — there are more.) The second stage game has three Nash equilibrium. The two pure are (A,a) and (B,b) and the mixed one has player 1(respectively 2) playA (respectivelya) with probability 3/4.
B) The players have four pure strategies in the rst stage game (two information setswith two actions in each). The second stage strategies can be conditional on theoutcomes of the rst stage, of which there are 4. (We are dening an outcome asthe payos of the rst stage and not the strategies that players chose to obtain thepayos. Unlike a matrix game, these will be dierent here because, as we saw inpart (a), there are dierent combinations of pure strategies that can lead to the sameoutcome.) Hence, there are 24= 16 pure strategies for each player in the second.
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