Econ 332, Economic Games and Strategy
Fall 2014, Exam #3
Dr. Stonebraker
Name ______________________________
1. (10%) Cody and Forrest play a game with payoffs as listed below.
Forrest
Cody
F1
F2
C1
44, 73
35, 90
C2
28, 36
78, 66
a. Are there any pure strategy Nash equilibriums if no strategic moves can be made? Explain.
b. Can one player improve his/her payoff by using a strategic move (commitment, threat or promise) or
combination of such moves? If so which player makes what move(s)?
2. (10%) One half of drivers on the road use cell phones while driving and have a 5% chance per year of
being in an accident. The other half does not use cell phones and has a 1% chance per year of being in
an accident. The cost of an accident is $20,000. Suppose the company cannot determine the relative
risks of drivers and so charges each driver a premium high enough for it to break even on an "average"
driver. What premium will it charge? What will happen? Explain clearly.
3. (5%) Stonebraker argues that consumers are not likely to benefit from a firm’s promise to match (or
beat) any price cuts by a rival competitor. Why? Is he crazy?
4. (5%) Why would anyone want to “burn their bridges”? Explain and give an example.
5.
(9%) A saleswoman insists that a product she wants to sell is of high quality, but she might be lying.
You will get $30 of value from buying if the product is of high quality, but lose $10 if it is not. You
estimate that the seller will earn $50 from the sale if the product is of high quality. If she is lying about
the quality, she will lose $30 in long-run sales from you, but will earn some amount ($X) in short-run
profits from the sale.
In other words, the payoff matrix is:
Seller
Tells truth
Buyer
Lies
Buy
30, 50
-10, -30 + X
Not buy
0, 0
0, 0
For what values of X will there be a cheap talk equilibrium? For what values of X will there be a
babbling equilibrium? Explain clearly.
6.
(10%) The Icelandic post-rock band Sigur Ros wants to help unemployed workers afford a ticket to its
upcoming concert. They decide to offer a $20 discount to anyone willing to wait in line to buy a ticket
at the box office instead of purchasing a ticket online. The dollar cost of waiting in line is t/(12) for an
unemployed worker and t/4 for an employed worker where is t = the number of minutes a person must
wait in line at the box office. What range of wait times will achieve separation of types?
7. (15%) Hershey’s wants to market its new chocolate hot dogs to the Food Lame Grocery chain. It
estimates it can earn a $100,000 profit margin on the contract. A sales representative who exerts low
effort will work for $10,000 and guarantees a 20% chance of getting the sale. For an extra $12,000 she
will exert high effort and guarantee a 60% chance of getting the sale.
a. Will paying for the extra sales effort be profitable for Hershey’s?
b. Suppose Hershey’s offers to pay the sales rep a flat $22,000 for high effort. What probably will
happen? Explain.
c. Suppose instead that Hershey’s pays the sales rep a base salary (S) plus a bonus (B). What minimum
bonus must it offer to get the sales rep to exert high effort? If it pays that B, what S must it pay?
Show your work.
8. (16%) An attacker is considering whether to invade a neighboring country but does not know if it will
encounter a weak or a strong defense. If it invades and the defender is weak, the attacker will gain 9 and
the defender, after a quick surrender will lose 6. If it invades and the defender is strong, a protracted war
will ensue in which both countries lose 12.
The defender is considering sending a signal that it will put up a strong defense. The cost of such a
signal to the defender is 4. In the absence of any credible signal, the attacker will assume there is a 60%
chance the defender is weak and a 40% chance it is strong.
a. Fill in the blanks in the game tree below with the payouts for the various possible outcomes (put the
defender’s payout first and the attacker’s second).
b. If there is no credible signal, should the attacker invade? Explain why or why not.
c. If the defender does send a signal, will it be credible? Explain why or why not.
Invade ____, ____
Attacker
Signal
Not invade ____, ____
Defender is weak
Invade ____, ____
No signal
Attacker
Not invade ____, ____
Nature
Invade ____, ____
Attacker
Signal
Not invade ____, ____
Defender is strong
Invade ____, ____
No signal
Attacker
Not invade ____, ____
9. (20%) The Plattsburgh Pilot baseball club can sell two types of seats to its games: standard (S) seats or
luxury (L) seats that come equipped with pillows, cup holders, and padded arm rests. It costs Plattsburgh
$4 to provide a regular seat and $8 to provide a luxury seat. It can sell to two types of customers:
wealthy fans who can more easily afford luxury seats, and poor fans who cannot. Wealthy fans
constitute p percent of the total potential buyers (B) and poor fans (1-p) percent.
The values of S and L seats to customers are:
S
L
Poor
$12
$15
Wealthy
$14
$22
a. Suppose Plattsburgh sells only L seats. It can charge $22 and sell only to wealthy fans or can drop
the price to $15 and sell to everyone. Under what conditions would it be more profitable to charge
$22? Show your work.
b. Suppose it makes both types of seats but cannot easily identify which fans are rich and which are
poor. If it wants to sell only L seats to rich fans and only S seats to poor fans, find the incentive
compatible prices for L and S that will separate the two groups of buyers and create the most profit.
Show your work.