Use the following normal-form game to answer the questions below. 

		Player 2
	Strategy	C	D
Player 1	A	10, 10	60, -5
	B	-5, 60	50, 50

 

a. Identify the one-shot Nash equilibrium.

b. Suppose the players know this game will be repeated exactly three times. Can they achieve payouts that are better than the one-shot Nash equilibrium? Explain.

c. Suppose this game is infinitely repeated and the interest rate is 5 percent. Can the players achieve payouts that are better than the one-shot Nash equilibrium? Explain.

Ans a)

In one shot game when both players choose to play simultaneously then when Player 1 chooses A Best response of Player 2 be C similarly when Player 2 chooses C then Best response of Player 1 is A

Hence we have only one Pure strategy Nash Equilibrium

(A,C)

Ans b)

Now when both players have complete information then these players will collude and both should choose as below

Player 1 chooses to play B and Player 2 chooses to play D in collusion because (B,D) is pareto efficient than (A,C) which is Nash Equilibrium.

Therefore with collusion both players can achieve payoffs higher than one shot Nash equilibrium

Ans C)

Now we need that player should play pareto optimal strategy in each round of game and not to deviate by playing other strategy than this one and if any of the player deviate then other player will start playing (A,C) henceforth This is possible only if

for player 1 or 2 we have

d=1/(1.05)=0.9523

50+60d+10d^2+10d^3+...=40+50d+10+10d+10d^2+...=40+50d+10/(1-d)=40+50(0.9523)+(10/0.0477)=297.259

And if no deviation is seen then

50+50d+50d^2+...=50/(1-d)=50/(0.0477)=1048.22

Hence when Discount rate is 5% then too player achieve higher payoff than one shot Nash equilibrium