Supplemental problems: 1. In each of the following three games, each player can

Question

Supplemental problems: 1. In each of the following three games, each player can choose between two actions, "cooperate" or defect" simultaneously. Suppose that in all three games, higher payoff numbers are preferred to lower payoff numbers. For each game, find all of the pure strategy Nash equilibria. Show/explain how you found these equilibria. If a pure strategy Nash equilibrium does not exist, indicate so. a. Prisoner's Dilemma Player 2 Defect 10,80 40.40 Coo Player 1 Cooperate Defect 80,10 b. Stag Hunt Player 2 70,70 40,5 Defect 5,40 40,40 Player 1 Looperate c. Chicken Player 2 Cooperate 70 80 Defect 50,80 40.40 Player 1 Cooperate Defect Q Search or enter website name 6

Explanation / Answer

(a) Prisoner's Dilemma :

When player 1 choose to COOPERATE , then player 2 has more pay off in choose to DEFECT.

When player 1 choose to DEFECT , then player 2 has more payoff in choose to DEFECT.

And when player 2 choose to COOPERATE then player 1 has more pay off in choose to DEFECT.

And when player 2 choose to DEFECT ,then player 1 has more pay off in choose to DEFECT.

Hence, the pure strategy Nash equilibrium is (DEFECT, DEFECT) i.e ( 40,40).

(b) Stag hunt:

When player 1 choose to COOPERATE , then player 2 has more pay off in choose to COOPERATE.

And when player 1 choose to DEFECT , then player 2 has more pay off in choose to DEFECT.

When player 2 choose to COOPERATE , then player 1 has more pay off in choose to COOPERATE.

And when player 2 choose to DEFECT , then player 1 has more pay off in choose to DEFECT.

Hence, there are two pure strategy Nash equilibrium (COOPERATE, COOPERATE) and (DEFECT, DEFECT).

(c) Chicken:

When player 1 choose to COOPERATE, then player 2 has more pay off in choose to DEFECT.

And when player 1 choose to DEFECT , then player 2 has more pay off in choose to COOPERATE.

When player 2 choose to COOPERATE, the player 1 has more pay off in choose to DEFECT.

And when player 2 choose to DEFECT then , player 1 has more pay off in choose to COOPERATE.

Hence, there are two pure strategy nash equilibrium : (COOPERATE, DEFECT) and (DEFECT ,COOPERATE)

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