Use the following normal-form game to answer the questions below. Player 2 Strat
ID: 1126321 • Letter: U
Question
Use the following normal-form game to answer the questions below.
Player 2
Strategy
C
D
Player 1
A
20, 20
60, 10
B
10, 60
25, 25
a. Identify the one-shot Nash equilibrium.
(Click to select)(B,D)(A,D)(B,C)(A,C)
b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium?
(Click to select)YesNo
c. Suppose this game is infinitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium?
(Click to select)YesNo
d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is . If is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?
(Click to select)YesNo
Player 2
Strategy
C
D
Player 1
A
20, 20
60, 10
B
10, 60
25, 25
Explanation / Answer
Use the following normal-form game to answer the questions below.
Player 2
Strategy
C
D
Player 1
A
20, 20
60, 10
B
10, 60
25, 25
a. Identify the one-shot Nash equilibrium
The Nash Equilibrium:- (A,C)
b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium?
No. This is a finitely played game with 3 rounds. Players know that round 3 is the last round, so they will treat that as a one shot game (or as if there is no tomorrow). Therefore, they both cheat in round 3. Because they know they will both cheat in round 3 and that they can't punish them for it in a future round, they cheat in round 2. This continues to unravel and they cheat in every round.
c. Suppose this game is infinitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium?
If firms adopt the trigger strategies outlined in the text, higher payoffs can be achieved if (Cheat - Coop) / (Coop - N) (1 / i) . Here, Cheat = 60, Coop = 25, N = 20, and the interest rate is i = 0.06. Since (Cheat - Coop) / (Coop - N) = (60 – 25) / (25 – 20) = 6.00 < (1 / i) = 16.67, each firm can indeed earn a payoff of 25 via the trigger strategies.
d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is . If is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?
Yes. With sufficiently low, this resembles the infinitely repeated game.
Player 2
Strategy
C
D
Player 1
A
20, 20
60, 10
B
10, 60
25, 25