(3) Team Coordination [28 Points]. Bob and Ann choose how much effort to put int

Question

(3) Team Coordination [28 Points]. Bob and Ann choose how much effort to put into a project. If they both work hard, the project is successful and both earn 100. If they both shirk, the project fails and the payoffs are 60. The project also fails if only one of them shirks; but then the party who worked hard loses 60 and ends up with a payoff of 0 Ann Work Hard 100, 100 60.0 Shirk 0. 60 60, 60 Bob Work Hard Shirk (a) What are the pure-strategy Nash Equilibria of the game? If there is more than one pure strategy Nash Equilibrium, make sure you specify all of them. Which equilibrium maximizes the payoffs of both players? (There is also a mixed-strategy Nash Equilibrium, but you don't need to compute it.)

Explanation / Answer

a) If Bob chooses to work hard then the best response of Ann is to work hard because it gives him more payoff i.e 100 which is greater than 60.

If Ann chooses to work hard then the best response of Bob is also to work hard because of higher payoff.

so, (work hard; work hard) is the nash equilibrium.

If Bob chooses to shrink then best response of Ann is to shrink otherwise it will give him payoff of zero.

If Ann chooses to shrink then best response of Bob is also to shrink because of higher payoff.

So, (shrink, shrink) is also the nash equilibrium.

Payoff of both players are maximum when both chooses to work hard.

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