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Chapter 13
Game Theory
Chapter Outline
13.1 Static Games
Normal–Form Games
Dominant Strategies
Best Response and Nash Equilibrium
Failure to Maximize Joint Profits
Application: Strategic Advertising
Multiple Equilibria
Solved Problem 13.1
Mixed Strategies
Application: Tough Love
Solved Problem 13.2
13.2 Dynamic Games
Repeated Games
Sequential Game
Game Tree
Subgame Perfect Nash Equilibrium
Credibility
Dynamic Entry Game
Solved Problem 13.3
Application: First Mover Advantages and Disadvantages
13.3 Auctions
Elements of Auctions
Number of Units
Format
Value
Bidding Strategies in Private-Value Auctions
Second-Price Auction Strategies
English Auction Strategy
Equivalence of Auction Outcomes
Winner’s Curse
Application: Bidder’s Curse
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13.4 Behavioral Game Theory
Application: GM’s Ultimatum
An Experiment
Reciprocity
Teaching Tips
Chapter 13 is one that you may want to cover in detail, especially if you have a significant number of
management majors or pre-MBA students. Some students view economic analysis, game theory in
particular, and management strategy as separate entities. The value of this material is that it links pricing
strategy, advertising profits, and entry decisions, and thus demonstrates the importance of understanding
microeconomic theory for good managerial decision making.
The chapter begins with an overview of the game theory and then moves on to static games, where players
must move simultaneously. It then reviews mixed strategies and dynamic games. There is a substantial
amount of self-teaching that can occur by having the class work in groups on selected problems (see
Additional Questions and Problems later in this chapter) designed to make the points from each section. If
the class has to work out the rules for effective strategy on their own, they are more likely to understand
why such rules for behavior are important.
When presenting game theory, consider dividing the class into small groups before making any formal
presentation of types of equilibria and strategic rules. Give each group three or four games to solve, including
a simple zero-sum game, a dominant strategy equilibrium where players follow a given strategy no matter
what the other does, and a Nash equilibrium where the payoffs create a prisoners’ dilemma. (The Additional
Questions and Problems section includes sample payoff matrices.) You can ask the groups to simply play
the games at first, under the following rules. First, assume that each player must move simultaneously and
that no cooperation is allowed. Second, allow collusion between players, and last, assume that one player
gets to move first. Finally, you could ask the groups to try to write down general decision-making rules for
players, and note whether they need to modify those rules when the game is played repeatedly. If you try
this, you may find that students are quite good at identifying strategic decision–making rules once they
understand the games. By asking students to play the games first, you can then go back through the various
outcomes and identify them as Cournot, cartel, and so on when you reach Chapter 14. One of the great
advantages of game theory is that by simply changing the rules, the same payoff matrix can be evaluated
more than once, with different outcomes. You can return to this discussion when covering the final section
of the chapter on the comparison of output, price, and welfare effects for the various models.
In the section that covers dynamic entry games, three points are worth emphasizing. The first is to be able
to evaluate if the incumbent firm needs to deter entry, if they would want to deter entry, or if they should
not act to do so. The second is to determine if the firm would be able to deter entry should they choose to.
Finally, you may want to engage the class in a discussion of the normative aspects of this strategy. Some
firms actively attempt to damage another firm’s reputation or raise their cost in order to gain advantage.
A similar but more widely accepted strategy is an advertising campaign where competing products are
“shown” to be inferior in consumer tests. Without discussing how the relevant law reads in this area, you
can ask students how they believe the law should read. What rules should firms have to abide by in a
competition over a local market? Which behaviors should be allowed here and which should be illegal is
likely to be a matter of debate within the class.
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Additional Applications
Electric Utilities1
In 1996, the Federal Energy Regulatory Commission ordered electric utilities to open up their transmission
systems to outside energy producers. The ruling allows for competition in the sale of wholesale power
to firms.
Of the 166 large utilities under the commission’s jurisdiction, 106 had already taken steps to open their
transmission at the time of the order. The ruling, however, requires utilities to set the same conditions in
transmitting power for others as they do for themselves, to reserve transmission capacity for outside power
producers, to disclose prices for moving power, and to post information on the Internet about access to
distribution systems.
This order should permit low-cost energy producers, like utilities in the Midwest, to use the national
network to deliver electricity to high–cost areas, such as the Northeast. In 1995, the average price per
kilowatt–hour of electricity in the Midwest was 6 cents compared to 10.4 cents in New England. According
to some estimates, this ruling may lower electric bills by between $3.8 and $5.4 billion dollars per year.
1. Assuming the New England and Midwest power companies both produce using technologies that are
characterized by extensive scale economies, what can you predict about the future of these firms?
2. What other strategies might New England power use to raise the costs of Midwest power companies in
order to remain competitive?
Horizontal Mergers Create Entry Deterrence in the Airline Industry2
The following excerpts from U.S. v. Northwest Airlines and Continental Airlines provides a glimpse into
the U.S. Department of Justice’s (DOJ) view on mergers as an entry deterrent. The ability of new and
existing carriers to enter new markets (routes) was a fundamental assumption of the initial deregulation of
the airline industry in 1978. The DOJ now appears quite concerned about strategic mergers that might
deter entry and thus limit competition.
“Under the “hub-and-spoke” system, an airline concentrates passengers from many points at the “hub”
location, then provides nonstop service from the hub airport to a large number of destinations (the “spokes”).
The hub-and-spoke system allows a carrier to serve more city pairs with more frequencies than would be
profitable on a stand-alone basis.
In seven hub-to-hub city pair markets, Northwest and Continental together dominate the market for
nonstop service and for all scheduled airline passenger service. These markets are Detroit-Cleveland,
Detroit–New York City, Detroit-Houston, Cleveland-Minneapolis, Minneapolis-New York City, Houston-
Minneapolis, and Houston-Memphis. Northwest and Continental’s market shares for nonstop flights in
each of the seven hub–to–hub city pairs are:
1Agis Salpukas, “Electric Utilities Ordered to Open Distribution Systems to Rivals,” San Fransisco Chronicle, April 25, 1996:A3;
and “Utilities Unbound: Get Your Kilowatts Here!” New York Times, April 28, 1996:S3, 2.
2http://www usdoj.gov/atr/cases/f2000/2023.htm.
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Northwest/Continental Hub-to-Hub Nonstop Shares
Route
NW Share
of Nonstop
Fights
CO Share
of Nonstop
Flights
Combined NW & CO
Share of Nonstop
Flights
Detroit
–Cleveland 54% 40% 94%
Detroit
–New York 70% 17% 87%
Detroit-Houston
36%
64%
100%
Cleveland
-Minneapolis 53% 47% 100%
Minneapolis
–New York 80% 20% 100%
Houston-Minneapolis
42%
58%
100%
Houston
-Memphis 39% 61% 100%
In two other hub-to-hub markets, Memphis-Newark and Cleveland–Memphis, Northwest currently has a
nonstop monopoly. As the only airline with a hub at the other endpoint, Continental is the most likely
potential entrant to challenge Northwest’s nonstop monopoly.
In total, nearly four million passengers travel in the nine hub-to-hub city pairs annually, generating
revenues of nearly $400 million per year.
Effective new entry for the provision of nonstop service in the hub–to–hub markets is unlikely by any carrier
without a hub at one of the endpoints of the city pair. A hub carrier, such as Northwest or Continental, has
significant cost advantages over a nonhub carrier attempting to offer service originating at the hub airport.
Building a competing hub in the same city would require considerable time and investment and is not
likely to occur in response to fare increases in the hub–to–hub markets at issue here.
New entry also is impeded by other factors, including difficulty in obtaining access to gate facilities, the
effects of travel agent incentive programs offered by dominant incumbents, frequent flyer programs, and
the risk of aggressive responses to new entry by the dominant incumbent carrier serving a particular market.
In addition to the hub–to-hub routes where Northwest and Continental share a virtual duopoly, Northwest
and Continental have a large share of the passengers traveling on connecting flights in numerous city pair
markets. Because of the light traffic on these routes and the short flights to the Northwest or Continental
hubs, carriers with more distant hubs are unlikely to initiate or expand competitive service to these
destinations from their hubs in response to significant fare increases.
1. Why do you suppose that having a hub and gate facilities in one of the city pairs is so important?
2. Log on to the DOJ website (http://www.usdoj.gov/atr), locate this case under “Antitrust Filings,” and
determine how it was finally resolved.
Discussion Questions
1. Give as many examples as you can of situations where an incumbent firm may have a strategic
advantage over a potential entrant.
2. Give as many examples as you can of situations where an entrant may have a strategic advantage
over an incumbent firm. (Is it ever an advantage to be small, or to not have sunk fixed costs already?)
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3. Can we distinguish between cooperative and noncooperative strategic behavior?
4. How can governments behave strategically toward other governments or firms? Explain.
5. What can firms do to make credible commitments?
6. List as many ways as you can in which a firm can raise its rivals’ costs.
7. Can it ever pay for a firm to take an action that raises its own costs more than those of its rivals?
8. If a prisoner’s dilemma game is played repeatedly with almost perfect information (see section on
Repeated Games) by several players, would a cooperative or noncooperative strategy be a winning
strategy? (Note: This is a reference to the Axelrod Tournament.)
9. Does advertising help or hurt consumers? Does it depend on the nature of the ads?
10. Does an advertisement that contains information about product characteristics and prices help
consumers or harm them? Why?
11. Are there any limitations to where auctions can be used as a price–discovery mechanism?
12. Can an auction be designed poorly? What is a “poorly designed auction,” in your opinion?
Additional Questions and Problems
1. In the following payoff matrix, each firm has two possible strategies, and must move simultaneously.
Assuming that each knows only its own payoff structure, what decision would each firm make? Is
this a Nash equilibrium? Suppose each player can see the entire payoff structure instead of only its
own. How would this affect Firm 2? Payoffs shown are (Firm 1, Firm 2):
Firm 2
A
B
Firm 1
A 3, 1 2, 0
B
2, 4 1, 5
2. In the following game, players must move simultaneously. How many Nash equilibria are there?
Which will occur without collusion? Which will occur if collusion is allowed?
Firm 2
A B
Firm 1
A 3, 1 7, 0
B
2, 4
5, 3
3. In the following game, assume that you are an interested bystander (such as the local government in
the town where Firm 1 is located). Can either firm make a credible commitment to enter? How could
you alter the incentives (payoffs) with a non-firm–specific prize to ensure that Firm 1 enters the
market? Under what circumstances would it be worth it to do so?
Firm 2
Enter
Don’t enter
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Firm 1
Enter −1, −2 4, 0
Don’t enter 0, 4 0, 0
4. Two firms are considering entering a new market. Entrance requires construction of a highly
specialized plant. Demand is sufficient for either one to be profitable but not both. A newspaper
writer, observing the posturing of the two firms, each stating that they are planning to go ahead with
plans for the new facility, noted, “sunk costs make for credible threats.” What does she mean by this
statement?
5. Suppose an industry has one incumbent and three potential new entrants. Any firm can produce as the
incumbent does, with no fixed costs, and marginal cost MC = bq. Is entry blockaded? Can/should it
be deterred? What type of equilibrium will result?
6. A monopolist faces demand p = 20 – Q + 0.5A0.5. Cost is C = 4Q + A, where A is the quantity of
advertisement, measured in $1 units. What are the profit-maximizing output and advertising levels?
What are the profits?
7. What are the merits and disadvantages to developing word processing software that has a very
different command structure than others on the market?
8. Show that if learning by doing results in the incumbent firm having the cost function C = 100 + 5Q0.5,
the firm does not need any further action to deter entry.
9. Suppose the French fry market is a duopoly. Tests show that 95 percent of consumers prefer Brand X.
Could it ever be shown that Brand Z is preferred in taste tests? What does this imply about such tests?
10. Jerry has the only ice cream store in town. There are only two methods of ice cream advertising that
work: billboards and radio ads. Billboards are cheaper but less effective than radio. Upon learning
that Ben will soon open a rival store, Jerry immediately rents all available billboard space. Why might
he choose this strategy? Under what circumstances will it be effective?
Answers to Additional Questions and Problems
1. Firm 1 has a dominant strategy of A. However, without knowledge of the other player’s possible
outcomes, Firm 2 must guess, as they do not have a dominant strategy. The solution (A, A) is a Nash
equilibrium, but (A, B) is not, since Firm 2 would rather switch, given Firm 1’s choice of strategy A.
If they can each see the entire matrix before play, Firm 2 will select strategy A rather than having to
guess Firm 1’s choice.
2. Each player has the dominant solution of strategy A, which is the only Nash equilibrium, and will
occur if collusion is not allowed. However, if collusion is allowed, (B, B) will be the outcome, even
though it is not a Nash equilibrium.
3. As the matrix is written, neither player has a dominant strategy nor can they make a credible threat of
entry, since each loses if both enter. However, if the local government offers a $1 prize to any firm
that enters the market, Firm 1 can make a credible threat of entry.