Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Solutions to Chapter 8 Exercises
UNSOLVED EXERCISES
U1. (a) Jack’s expected utility is 0.5 • √250,000 + 0.5 • √90,000 = 400.
(d) Under the agreement, the expected utility for each participant is 0.25 • √250,000 + 0.25 •
√170,000 + 0.25 • √170,000 + 0.25 • √90,000 ≈ 406.1552.
(f) The eight possible luck outcome triplets for Jack, Janet, and Chrissy are (good, good,
(g) Under the agreement, the expected utility for each participant is 0.125 • √250,000 + 3 •
(h) For Jack, Jill, or Chrissy to achieve a utility of 408.2744, he or she (or she) would need a
U2. (a) Month 1:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Willingness to accept
of sellers
Willingness to pay
of buyers
Month 2:
Willingness to accept
of sellers
Willingness to pay
of buyers
Month 3:
Willingness to accept
of sellers
Willingness to pay
of buyers
(b) Risk-neutral buyers of a citrus of unknown type are willing to pay up to 0.8 • (willingness
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
$10,000
$10,500
$11,000
$11,500
$12,000
$12,500
$13,000
$13,500
$14,000
1 2 3 4 5 6 7 8 9 10 11 12
Price
Month
willingness to accept of orange
sellers
willingness to pay of buyers of an
unknown Citrus type
(c) Yes, there is a market for oranges in month 3, since the willingness to pay of buyers for
(d) The market for oranges collapses in month 6, when the willingness to pay of the buyers
(e) Whether or not lemons depreciate for potential sellers of lemons does not affect the
(f) Depreciation of lemons among potential buyers of a citrus of unknown type does affect
the timing of the collapse of the market for oranges. If lemons never depreciate among buyers, their
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U3. (a) To achieve separation, the incentive compatibility conditions are
(b) If the signal is not available, then every worker is treated like a random draw from the
U4. (a) In a separating equilibrium, St. Anford will set a threshold number of publications to
determine whether it will grant tenure. Brilliant professors will signal their type by reaching that
(b) One pooling equilibrium has both Brilliant and Good types not applying for tenure at St.
A second pooling equilibrium has both types applying for and being granted tenure. In this case N
(c) To achieve a separation of types both of the following inequalities must hold:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
The first inequality implies that N < 50, while the second implies that N > 25. Any number of publications
N in the set (25, 50) will achieve a separation of professor types for St. Anford.
U5. (a) In terms of z, Figure 8.10 is shown in the table below:
Fordor
Regardless (II) Conditional (OI)
(b) When z = 0 (that is, when Tudor is definitely high cost), the game table is as follows:
Fordor
Regardless (II) Conditional (OI)
There is only one pure-strategy Nash equilibrium: (Honest, Regardless).
The equilibrium found in the previous figure is separating. The two types of Tudor charge
(c) When z = 1 (that is, when Tudor is definitely low cost), the game table is as shown below:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Fordor
Regardless (II) Conditional (OI)
There are two pure-strategy Nash equilibria: (Bluff, Conditional) and (Honest, Conditional). (Bluff,
Conditional) is a pooling equilibrium, since both Tudor types charge the same price in the first period.
(d) There are two possible pooling equilibria: (Bluff, Regardless) and (Bluff, Conditional).
Next consider the pooling equilibrium (Bluff, Conditional). Fordor will play Conditional if 0 ≥
(e) If z is too low, Fordor can be fairly confident that Tudor is high cost, and so Fordor will
U6. (a) The game tree for a risk-averse Tudor with a low per-unit cost of 10 follows:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(b) If the probability that Tudor is low cost is z = 0.4, the game table for the previous game
tree is as follows:
Fordor
Regardless (II) Conditional (OI)
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Nature
Tudor’s
cost high
Prob. 0.6
Tudor
Price
low
Price
high
Fordor
Fordor
In
Out
5 + √3 , 5
In
Out
√19 + √3 , 5
√19 + √3 , 0
(–15) • 0.4 + 5 • 0.6 = –3
The unique Nash equilibrium is (Bluff, Conditional). Since both Tudor types send the same signal (they
both set low prices in the first period), this is a pooling equilibrium.
(c) If z = 0.1, the payoffs in the game table become
Fordor
Regardless (II) Conditional (OI)
Here, the unique Nash equilibrium is (Honest, Regardless), which is a separating equilibrium.
(d) Tudor’s risk aversion will not affect the threshold level of z required for a pooling
U7. (a) When Tudor’s low per-unit cost is 6 and its probability of being low cost is z, the game
table is as follows:
Fordor
Regardless (II) Conditional (OI)
(b) When z = 0.1, the payoffs are as follows:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Fordor
Regardless (II) Conditional (OI)
The equilibrium is (Honest, Regardless). It is a separating equilibrium because the two types of Tudor
send different signals according to their type.
(c) When z = 0.2, the payoffs are as follows:
Fordor
Regardless (II) Conditional (OI)
Here the equilibrium is (Bluff, Conditional). It is a pooling equilibrium because both types of Tudor send
the same signal regardless of their type.
(d) When z = 0.3, the payoffs are as follows:
Fordor
Regardless (II) Conditional (OI)
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
The equilibrium is again the pooling equilibrium (Bluff, Conditional).
(e) In part (d) of Exercise U5, the lowest z for which a pooling equilibria could occur was
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
