Problem 3: A Coordination Game Two people can perform a task if, and only if, they...

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Problem 3: A Coordination Game Two people can perform a task if, and only if, they both exert effort. They are both better off if they both exert effort and perform the task than if neither exerts effort (and Player 2 LR T 0,1 0,2 Player 1 B 2,2 0,1 Table 2: The Game nothing is accomplished); the worst outcome for each person is that she exerts effort and the other person does not (in which case again nothing is accomplished). Specifically, the players' preferences are represented by the expected value of the payoff functions in table 3, where c is a positive number less than 1 that can be interpreted as the cost of exerting effort. Find all the mixed strategy Nash Equilibria of this game. How do the equilibria change as c increases? Explain the reasons for the changes. Player 2 No Effort Effort No Effort 0,0 0,-c Player 1 Effort -c,0 1-c,1-c Table 3: The Game Problem 3: A Coordination Game Two people can perform a task if, and only if, they both exert effort. They are both better off if they both exert effort and perform the task than if neither exerts effort (and Player 2 LR T 0,1 0,2 Player 1 B 2,2 0,1 Table 2: The Game nothing is accomplished); the worst outcome for each person is that she exerts effort and the other person does not (in which case again nothing is accomplished). Specifically, the players' preferences are represented by the expected value of the payoff functions in table 3, where c is a positive number less than 1 that can be interpreted as the cost of exerting effort. Find all the mixed strategy Nash Equilibria of this game. How do the equilibria change as c increases? Explain the reasons for the changes. Player 2 No Effort Effort No Effort 0,0 0,-c Player 1 Effort -c,0 1-c,1-c Table 3: The Game