In the incomplete information version of the Game of Chicken (see Tadelis 2013, Section 12.2.1), players 1 and 2 drive toward each other and just before impact they simultaneously decide whether to swerve to the right or continue driving head-on." If both play chicken, each gets a payoff of 0. If i continues to drive while j # i plays chicken, then i get a payoff of 8 and j gets a payoff of 0. Finally, if both continue to drive head-on, then each gets 4 – k, where k represents the cost to each player. k could be, with equal probability, either high or low. While the distribution of type is common knowledge, none of the two players knows whether the cost to the other player is high or low. 1. Denoting the high cost with H and the low cost with L, draw the extensive form of the game. 2. Assuming H= 16 and L = 0, derive from the extensive form the normal form, and find the unique pure-strategy Bayesian Nash equilibrium.
In the incomplete information version of the Game of Chicken (see Tadelis 2013, Section 12.2.1), players 1 and 2 drive toward each other and just before impact they simultaneously decide whether to swerve to the right or continue driving head-on." If both play chicken, each gets a payoff of 0. If i continues to drive while j # i plays chicken, then i get a payoff of 8 and j gets a payoff of 0. Finally, if both continue to drive head-on, then each gets 4 – k, where k represents the cost to each player. k could be, with equal probability, either high or low. While the distribution of type is common knowledge, none of the two players knows whether the cost to the other player is high or low. 1. Denoting the high cost with H and the low cost with L, draw the extensive form of the game. 2. Assuming H= 16 and L = 0, derive from the extensive form the normal form, and find the unique pure-strategy Bayesian Nash equilibrium.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.7P
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