1
Economics 1200 Fall 2008
Answers to Homework # 2
1. a) [1 point] As in the example in class, suppose the first mover, Player 1, is the
buyer, and the second mover, Player 2, is the seller. In a two round game, Player
1 knows that Player 2, will propose to keep the entire difference, M=$12,000, for
herself in the second and final round. Since the period discount factor δ=.2, Player
1 knows he must give Player 2 δ×$12,000 in round 1 to maker Player 2 indifferent
between accepting in round 1 or waiting to make a counterproposal in round 2,
Thus, Player 1 proposes in round 1 that Player 2 gets (.2)$12,000=$2,400, and
Player 1 gets the remainder, $12,000-$2,400=$9,600 for himself. Player 2 agrees
since there is no benefit to be gained by waiting. Since Player 1 is assumed to be
the buyer, the equilibrium sale price for the home is $188,000+$2,400=$190,400.
If instead Player 1 was assumed to be the seller and Player 2 the buyer, then the
equilibrium sale price for the home would be $200,000-$2,400=$197,600.
b) [1 point] In the infinitely repeated game, we showed in class that if Player 1
(the buyer) moves first, he will propose to keep [(1-d)/(1-d2)]M for himself with
the remainder going to Player 2 (the seller). This proposal will be made in the first
round and is acceptable to Player 2. With δ=.2 player 1 (the buyer) will propose to
keep [(1-.2)/(1-(.2)2)] 12,000 = (5/6)(12,000) = $10,000 for himself with the
remainder, $2,000 going to player 2 (the seller). So the equilibrium sale price in
this case is $190,000 ($188,000+$2,000). Player 1 would prefer an infinite
number of rounds to just a single round since he gets to keep slightly more of M
($400 more) for himself if he is the first mover.
2. a) [1 point] For prisoner’s dilemma, you can use elimination of dominated
strategies or best-response analysis. The only (unique) pure strategy Nash
equilibrium is: Defect, Defect, with a payoff of 40,40.
b) [1 point] In stag hunt, there are two pure strategy Nash equilibria which you
can find by best response analysis. These are: Cooperate, Cooperate with a payoff
of 70,70 and Defect, Defect with a payoff of 40, 40.
c) [1 point] In chicken, there are two pure strategy Nash equilibria which you can
find by best response analysis. These are: Cooperate, Defect with a payoff of
50,80 and Defect, Cooperate with a payoff of 80, 50.
3. a) [1/2 point] Assigning a payoff of 4 to best, 3 to second best, 2 to third best and
1 to worst, the normal form of this game would be written as:
