Solutions to Chapter 3 Exercises
UNSOLVED EXERCISES
U1.
A first-mover advantage is not a necessary property of sequential games. There are sequential
games with a first-mover advantage, a second-mover advantage, or no advantage. Consider the matchstick
ga
Solutions to Chapter 7 Exercises SOLVED EXERCISES
S1. False. A players equilibrium mixture is devised in order to keep her opponent indifferent
among all of her (the opponents) possible mixed strategies; thus, a players equilibrium mixture yields the oppo
Solutions to Chapter 11 Exercises SOLVED EXERCISES
S1. False. The players are not assured that they will reach the cooperative outcome. Rollback
reasoning shows that the subgame-perfect equilibrium of a finitely played repeated prisoners dilemma will enta
Solutions to Chapter 5 Exercises SOLVED EXERCISES
S1. (a) Rs best-response rule is given by y = 10x x. L spends $16 million, so x = 16. Then
Rs best response is y = 1016 16 = 10(4) 16 = 40 16 = 24, or $24 million. (b) simultaneously: x = 10(10x x)1/2 10x
Solutions to Chapter 9 Exercises SOLVED EXERCISES
S1. (a) Your neighbor has a sure income of $100,000. In addition, under the insurance
contract, he will receive x when you have a good year and pay you $60,000 when you have a bad year. The lowest value of
Principal Agent Problem Set
1) An owner (the principal) employs a manager (the agent) to run a restaurant. The
manager can exert high effort or low effort in running the restaurant. Putting in high effort
costs 2 (i.e. it deducts 2 from his utility), whil
Solutions to Chapter 4 Exercises
UNSOLVED EXERCISES
U1.
(a)
Left dominates Right for Column, so Right is eliminated. With only Left, Down dominates
Up for Row, so the pure-strategy Nash equilibrium is (Down, Left).
(b)
Down is a dominant strategy for Row,
Solutions to Chapter 6 Exercises
UNSOLVED EXERCISES
U1.
(a)
The game tree is shown at right.
The subgame-perfect equilibrium is (Down, Right).
(b)
The strategic form of this game is shown below.
Player B
If Down,
If Down, then
then Left
Right
Up
2, 2
2, 2
Solutions to Chapter 7 Exercises
UNSOLVED EXERCISES
U1.
Find Nash equilibria in mixed strategies for the following games.
(a)
4p 1(1 p) = p 2(1 p)
p = 1/6
4q 1(1 q) = q + 2(1 q)
q = 1/2
The mixed-strategy Nash equilibrium is:
Row plays 1/6(Up) + 5/6(Down)
Solutions to Chapter 4 Exercises SOLVED EXERCISES
S1. False. A dominant strategy yields you the highest payoff available to you against each of your
opponents strategies. Playing a dominant strategy does not guarantee that you end up with the highest of a
Solutions to Chapter 2 Exercises SOLVED EXERCISES
S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is
simply making a decision. If some flavors of yogurt were in short supply, then it would be a game, because shop
Solutions to Chapter 18 Exercises SOLVED EXERCISES
S1. The father and daughter were implicitly negotiating about how much freedom from parental
control she would have. The fathers BATNA was low: breakdown of negotiation would lead to a tantrum or a scene
Solutions to Chapter 5 Exercises
UNSOLVED EXERCISES
U1.
(a)
DTCs profit is YDTC = PQDTC 12QDTC = (120 QDTC)QDTC 12QDTC = QDTC2 + 108QDTC.
The profit-maximizing quantity for DTC is QDTC = 54.
At this profit-maximizing quantity, the wholesale price is given
Solutions to Chapter 6 Exercises SOLVED EXERCISES
S1. Second-mover advantage. In a sequential game of tennis, the second mover will be able to
respond best to the first movers chosen action. Put another way, the second mover will be able to exploit the in
Solutions to Chapter 14 Exercises
UNSOLVED EXERCISES
U1.
(a)
Asymmetric information can lead to pronounced problems of moral hazard when a broker
sells financial services or products such as stocks, mutual funds, or mortgages. (Recall the simplified
examp
Solutions to Chapter 9 Exercises
UNSOLVED EXERCISES
U1.
(a)
Jacks expected utility is 0.5 250,000 + 0.5 90,000 = 400.
(b)
Since Jacks utility is the square root of his income, to achieve a utility of 400 Jack would
need a certain income of 4002 = $160,000
Solutions to Chapter 10 Exercises SOLVED EXERCISES
S1. The statement is true because promises, when successfully used as strategic moves, require that
you follow through on the promised action; you will not promise an arbitrarily large reward. You may thr
Solutions to Chapter 8 Exercises SOLVED EXERCISES
S1. False. A players equilibrium mixture is devised in order to keep her opponent indifferent among
all of her (the opponents) possible mixed strategies; thus, a players equilibrium mixture yields the oppo
Solutions to Chapter 15 Exercises SOLVED EXERCISES
S1. (a) In the pure-threat case, the unions expected payoff is 50(1 p) 100p = 50 150p. The
unions expected payoff goes to zero for p = 1/3 and is negative for p > 1/3. Thus the pure threat is too big from
Solutions to Chapter 14 Exercises SOLVED EXERCISES
S1. Some examples of incentive schemes that help induce more care on the part of policy holders: 1. The insurer can provide a multiyear contract or otherwise establishes an ongoing relationship in which f
Solutions to Chapter 19 Exercises SOLVED EXERCISES
S1. (a) The existence of buyer B2 means that buyer B1 will not be able to buy at any price below
200. If B1 tried to strike a deal at (for example) 190, B2 could offer to pay 191; if B2 bought at that pri
Solutions to Chapter 17 Exercises SOLVED EXERCISES
S1. The painter can compare her estimated cost to a jobs true cost only when she does the job. But
the painter does a job only when she agrees (through the bidding process) to do it for less than anybody
Solutions to Chapter 16 Exercises SOLVED EXERCISES
S1. Under truthful voting, A should match Geology and Sociology in the first vote, with the winner (Geology) to face Philosophy in the second round. Under strategic voting, A should match Philosophy and S
Solutions to Chapter 13 Exercises SOLVED EXERCISES
S1. (a) The payoff table for the two types of travelers is: High High Low 100, 100 70, 30 Low 30, 70 50, 50
(b)
The graph is:
(c)
There are three possible equilibria: a stable monomorphic equilibrium of a
Solutions to Chapter 12 Exercises SOLVED EXERCISES
S1. (a) (b) The number choosing X should decrease to move the population division between X and Because the line for action X is above the line for action Y when 100 people choose X,
Y away from the unsta