hw510 - 14.12 Game Theory Prof. Muhamet Yildiz Fall 2010...

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14.12 Game Theory Prof. Muhamet Yildiz Fall 2010 Homework 5 Due on 12/2/2010 (in class) Youneedtoshowyourworkina l lquest ions . 1. Consider the following two-player game in which the payo f s and the actions are as follows: LR U 2  0,0 D 0,0  2 Here, { 1 1 } and { 1 1 } are privately known by players 1 and 2, respectively, and the probability of each (  ) pair is 1/4. (a) Write this as a Bayesian game. (b) Find all pure-strategy Bayesian Nash equilibria of this game. Verify that they are indeed Bayesian Nash equilibria. 2. Two siblings, named Alice and Bob, have inherited a car from their parents. The car is “peach” with probability , in which case its value is ˆ  0 , but it may be a “lemon” with probability 1 , in which case its value is 0. They have equal shares on the car, but they would rather one of them owned the car. The ownership of the car is decided as follows. Alice o f
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hw510 - 14.12 Game Theory Prof. Muhamet Yildiz Fall 2010...

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