Self Test

Repeated Prisoner's Dilemmas & Trigger Strategies

Two firms are playing an infinitely-repeated prisoner's dilemma pricing game of the following form:

		Firm 2
		low	high
Firm 1	low	5 , 5	20 , 0
Firm 1	high	0 , 20	10 , 10

The firms simultaneously set prices at regular intervals. In the equilibrium of this game (if played only once), each firm selects the low price. However, the firms are playing this game repeatedly, for an infinite period of time. The firms utilize trigger strategies in order to maintain the collusive outcome.

Question 1.

Suppose that both firms adopt the grim trigger strategy. They continue charging the high price unless one of them cheats. Upon one of them charging the low price, they play the equilibrium, low-price strategy for the rest of the game. What has to be true about the interest rate (r) for cooperation to be sustainable?

	r < 25%
	r > 25%
	r < 50%
	r > 50%

Question 2.

Suppose that both firms adopt a tit-for-tat strategy. They initially charge the high price. In future periods, a firm charges the high price if its competitor did in the previous period, and elects the lower price if its competitor priced low in the previous period. What has to be true about the interest rate (r) for collusion to be sustainable?

	r < 50%
	r < 0%
	r > 25%
	r < 25%

Consider the following game:

		Kid's Corner
		High	Low
Child's Play	High	64 , 64	20 , 72
Child's Play	Low	72 , 20	57 , 57

Question 3.

If this game is repeated for a known length of four periods, what will be Child's Play average (per-period) payoff in the subgame-perfect equilibrium of this game?

	20
	57
	64
	72

Question 4.

If this game is repeated forever, and firms adopt a grim-trigger strategy, what has to be true about the interest rate for cooperation to be sustainable?

	r < 7/8
	r < 0
	r < 5
	r < 15/37

For each of the following games, determine if the game is a prisoner's dilemma.

Question 5.

		Player 2
		A	B
Player 1	X	10 , 10	8 , 4
Player 1	Y	4 , 8	7 , 7

	Game is a prisoner's dilemma
	Game is not a prisoner's dilemma

Question 6.

		Player 2
		A	B
Player 1	X	5 , 5	8 , 4
Player 1	Y	4 , 8	7 , 7

	Game is a prisoner's dilemma
	Game is not a prisoner's dilemma

Question 7.

		Player 2
		A	B
Player 1	X	5 , 5	4 , 4
Player 1	Y	4 , 8	7 , 7

	Game is a prisoner's dilemma
	Game is not a prisoner's dilemma

Question 8.

		Player 2
		A	B
Player 1	X	6 , 6	4 , 8
Player 1	Y	8 , 4	5 , 5

	Game is a prisoner's dilemma
	Game is not a prisoner's dilemma