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CHAPTER TEN
GAME THEORY AND
COMPETITIVE STRATEGY
OBJECTIVES
1. To identify the similarities and differences among competitive situations.
(Sizing up Competitive Situations)
2. To introduce game-theoretic analysis: payoff tables and equilibrium
strategies. (Analyzing Payoff Tables)
3. To explore competitive strategies: entry deterrence and settings involving
coordination and bargaining. (Competitive Strategy)
4. To analyze sequential and repeated competition (Sequential
Competition).
TEACHING SUGGESTIONS
I. Introduction and Motivation
There are numerous real-world examples of competitive situations that can
be usefully analyzed using game-theoretic logic. A good source of examples
is the current business press. (See the following list of suggested short
articles.) Besides the applications in the chapter, the instructor can also draw
on selected examples from Chapter 9 (oligopoly) and Chapter 15
(bargaining). Another option is to engage students in stylized business
games in class. See the competitive games described in Chapter 1 of this
manual and, in the present chapter, the Battle for Air Passengers (modified
with different revenues and costs) and the Shuttle Competition (Discussion
Question).
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II. Teaching the “Nuts and Bolts”
In our view, the most important ground to cover involves the creation and
analysis of payoff tables. The instructor should carefully walk the class
through the concepts of best responses, dominant strategies, and equilibrium
strategies (in both zero-sum and non-zero sum settings). Students find the
method of circles and squares particularly useful for finding equilibrium
strategies. With a good grasp of these foundations, students can move on to
the interesting “competitive strategy” applications. The analysis of game
trees (extensive form games) can also be emphasized. The notion of a
mixed strategy is an important optional topic presented in the appendix.
Suggestions
1. The payoff table in Check Station 3 (depicting quantity competition)
merits some discussion. (This is another look at the Cournot model
introduced in Chapter Nine and provides a nice link.) The instructor
should:
a. Walk through the firms’ best responses and establish the
non-cooperative equilibrium.
b. Contrast the cooperative and non-cooperative outcomes. The
collusive outcome is Q1 = Q2 = 6, where the firms’ total profits are
maximized.
After these points have been brought out, it is easy to derive algebraic
expressions for each player’s best response by setting MR = MC so that
[30-Q2] - 2Q1 = 6, or Q1 = 12 - .5Q2. In turn, the (Nash) equilibrium is
Q1 = Q2 = 8, after noting that Q1 must equal Q2 by symmetry.
2. Market share competition (Problem 10). This constant-sum game
requires students to construct the payoff table and identify the
dominant-strategy equilibrium. Spreadsheet Problem 2 provides an
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advanced extension: If each firm has $10 million dollars to divide
between the two markets, what is the equilibrium allocation?
Answer. Each should divide the $1 million in proportion to the size of the
markets. Market I gets 30/48 of the total; Market II gets 18/48 of the
total.
3. Battle for Air Passengers. Additional remarks.
i) As a “learning-by-doing” vehicle, this example can be played
competitively by students in class. For instance, 30 to 40 students might
be divided into 9 airline management teams with teams A, B, and C
competing in one market; D, E, and F in a second market; and G, H,
and I in a third. After 10 minutes of private discussion, each team writes
down its number of departures. The first-round results for each market
are posted on the blackboard, and profits are computed. With these
results in view, teams make new decisions in a second round, the results
are again posted, and then there is a third and final round. Since second
and third round decisions tend to be reached quickly, the entire exercise
(including discussion) takes about 45 to 60 minutes. Our rough track
record of results is as follows:
ii) We recommend that the instructor runs the exercise in class using
different economic facts (so that knowledge of the text answer doesn’t
dictate behavior), we suggest: R = $900,000, c = $25,000, and n = 3. In
addition, let the capacity per flight be 300 passengers and the total
number of passengers be 3,600. The collusive outcome is 3,600/300 =
12 total flights. From the formula above, the equilibrium outcome is 8
flights each (24 total). Finally, the zero-profit outcome occurs when
there are 36 total flights.
iii) In the battle using the new economic facts:
a. About 1 in 3 markets converge to equilibrium play (8, 8, 8) or near
to equilibrium (8, 8, 9) or (8, 8, 7) by the second or third round.
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b. About 1 in 7 markets find their way to the tacit collusion outcome
(4, 4, 4) or nearly there (4, 4, 5) or (4, 4, 6).
c. About 1 in 3 markets converge to the zero-profit outcome (12, 12,
12).
d. The remaining behavior is just plain random.
There is an interesting explanation for the zero-profit outcome. This
result inevitably occurs if teams look at relative profits rather than
absolute profits. As long as total industry profit is positive, the airline
with the most departures makes the most profit. (This is because both
revenues and costs are proportional to the number of departures.) For
example, if the first round result is (6, 8, 10), the respective profits are
75, 100, and 125. Looking at these profits, teams are often inclined to
add flights to chase the market leader. A second round result might be (9,
10, 10) and a third round result (10, 11, 12). These outcomes usually
prompt discussion of an airline’s “real” goal. Is it to maximize the
airline’s absolute level of profit? Or is it to earn more than its rivals? We
make it a point to emphasize at the outset of the exercise that all
shareholders care about is the firm’s absolute level of profit. (However,
the presumption could be quite different if the competition were
modeled as a dynamic “war of attrition.”)
iv) For the new economic facts, the calculus derivation of the equilibrium
is as follows:
πa = 900[a/(a + b + c)] - 25a.
Therefore, dπa/da = 900[(b + c)/(a + b + c)2 ] - 25 = 0.
By symmetry, a = b = c. Thus, we have: (900)(2a)/9a2 = 25, or a = 8.
In general, the equilibrium is: a = (R/c)(n-1)/n2, where R is total
revenue, c is the cost per flight, and n is the number of airlines.
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4. The Shuttle Battle (Discussion Question). This takes less than 20
minutes to play and discuss in class and is another real “eye opener” for
students. Be sure to prohibit students from any prior communicating.
Have students use a score sheet like the one on the next page. At each
round, students write down their chosen prices, reveal these to their
partners, and record profits.
Top performance occurs when both airlines aim for a collusive outcome
($139 fares) and neither deviates to lower fares until near the end of the
game. The worst performance occurs if one or both airlines engage in
cut-throat pricing in the early periods. Once this occurs, it becomes
nearly impossible to regain high-price ground.
Some benchmarks: $139 prices lead to payoffs of 612 and 684
respectively. In turn, $119 prices lead to a payoff of 396 for each airline.
Finally, $99 prices lead to payoffs of 324 and 288 respectively.
C. Recommended Problems
- Problems 3, 4, 6, 8, and 12
The Shuttle Battle
Delta played by ______________ US Air played by ___________
(Name) (Name)
US Air Prices
$139 $119 $99
Delta $139 34, 38 15, 42 6, 32
Prices $119 42, 20 22, 22 10, 25
$99 35, 7 27, 9 18, 16
Month Delta’s US Air’s Delta’s US Air’s
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Price Price Profit Profit
1 $ ___ $ ___ ___ ___
2 $ ___ $ ___ ___ ___
3 $ ___ $ ___ ___ ___
4 $ ___ $ ___ ___ ___
5 $ ___ $ ___ ___ ___
6 $ ___ $ ___ ___ ___
7 $ ___ $ ___ ___ ___
8 $ ___ $ ___ ___ ___
9 $ ___ $ ___ ___ ___
10 $ ___ $ ___ ___ ___
11 $ ___ $ ___ ___ ___
12 $ ___ $ ___ ___ ___
13 $ ___ $ ___ ___ ___
14 $ ___ $ ___ ___ ___
15 $ ___ $ ___ ___ ___
16 $ ___ $ ___ ___ ___
17 $ ___ $ ___ ___ ___
18 $ ___ $ ___ ___ ___
Total Profits ___ ___
ADDITIONAL MATERIALS
I. Short Readings
S. Carey, “Delta, Alaska go to War over Seattle,” The Wall Street Journal,
June 30, 2014, p. B1.
S. J. Levitt and S .J. Dubner, “How to Trick the Guilty and Gullible into
Revealing Themselves,” The Wall Street Journal, May 10, 2014, pp. C1, C2.
K. Seelye and J. Bidgood, “Officials back Deep Cuts in Atlantic Cod
Harvest to Save Industry,” The New York Times, January 31, 2013, p. A11.
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S. Ovide, G. Bensenger, and A. Efrati, “Tech Titans Clash in ‘Cloud’,” The
Wall Street Journal, February 4, 2013, p. B1.
J. Levitz and B. McKay, “Can a Whole City Stick to a Diet? Fat Chance,”
The Wall Street Journal, January 23, 2013, pp. A1, A12.
A. Mattioli, “Holiday Price War Rages in Real Time,” The Wall Street
Journal, November 24, 2012, pp. A1, A2.
A. Zimmerman, “We Promise to Match Prices,” The Wall Street Journal,
October 18, 2012, pp. B1, B4.
C. Rampell, “2 from US win Nobel in Economics,” The New York Times,
October 16, 2012, pp. B1, B5.
J. Jannarone and C. S. Stewart, “Sing-Off Duel Saps Ratings,” The Wall
Street Journal, October 1, 2012, p. B6.
P. O’Connor and S. Murray, “After the Celebrating, Race Moves to
Battleground States,” The Wall Street Journal, August 31, 2012.
K. Hudson, “Developers Duel over Malls in Missouri,” The Wall Street
Journal, August 8, 2012, p. B8.
B, Barnes, “Clash of the Theme Parks,” The New York Times, May 22, 2012,
pp. B1, B6.
N. King and L. Meckler, “Math Challenge for Romney,” The Wall Street
Journal, May 4, 2012, p. A4.
R. Stross, “A Strong Password isn’t the Strongest Security,” The New York
Times, September 5, 2010, p. BU3.
J. Surowiecki, “Priced to Go,” The New Yorker, November 9, 2009, p. 31.
J. E. Vascellaro and E. Smith, “Google and Microsoft Crank Up Rivalry,”
The Wall Street Journal, October 22, 2009, pp. B1, B2.
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C. Duhigg, “Stock Traders Find that Speed Pays, in Milliseconds,” The New
York Times, July 24, 2009, pp. A1, A15.
A. Frangos, “In Atlanta, Irrational Building,” The Wall Street Journal, April
22, 2009, p. C8.
K. Hudson, “Score One for Challenger in Phoenix’s Mall Bout,” The Wall
Street Journal, March 13, 2008, Pp. B1, B2
P. Cohen, “The Art of the Save, for Goalie and Investor,” The New York
Times, March 1, 2008.
R. Weisman, “X Games for Scientists Offers $10 Million Top Prize,” The
Boston Globe, December 4, 2007, Pp. C1, C4.
“Boeing versus Airbus,” The Economist, June 25, 2005, pp. 67-68.
C. Vogal, “Rock, paper, Payoff: Child’s Play Wins Auction House an Art
Sale,” New York Times, April 29, 2005, p. A1.
J. Lee, “And the Password is ….Waterloo,” The New York Times, December
27, 2001, p. D1.
L. Gomes, “QWERTY Spells a Saga of Market Economics,” The Wall Street
Journal, February 25, 1998, p. B1.
“Shuttle Diplomacy, Airline Style,” The New York Times, October 25, 1996,
p. D1. (This article describes how airlines compete for market share by
adding daily departures.)
II. Longer Readings
Clive Thompson, “Can Game Theory Predict When Iran will Get the
Bomb?” New York Times Magazine, August 16, 2009, pp. 20-25.
Alec Wilkinson, “What Would Jesus Bet?” The New Yorker, March 30,
2009, p. 30.
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V.Suslow, “Entry Deterrence Strategies,” Journal of Industrial Organization
Education, Vol. 1, 2006.
Silvia Nasar, A Beautiful Mind, Simon and Schuster, 2001.
This fine book chronicles the struggle with schizophrenia of 1994 Nobel
Prize winner, John Nash (a developer of game theory). The film of the same
name, starring Russell Crowe, is also of interest.
Symposium on Evolutionary Economics, Journal of Economic Perspectives,
Spring 2002, 23-106.
J. K. Goeree and C. A. Holt, “Ten Little Treasures of Game Theory and Ten
Intuitive Contradictions,” American Economic Review, 91, 2001, 1402-1422.
Malcom Gladwell, “The Tipping Point,” The New Yorker, June 3, 1996,
p. 32. (This article discusses the evolution and spread of disease and crime.)
Adam M. Brandenburger and Barry J. Nalebuff, “The Right Game: Use
Game Theory to Shape Strategy,” Harvard Business Review, July-August
1995, 57-71.
J. Stavins, “Firm Strategies in the Personal Computer Business: Are
Established Brands Better Off?” New England Economic Review,
November-December 1995, 12-24.
R. H. Frank, T. Gilovich, and D. T. Regan, “Does Studying Economics
Inhibit Cooperation?” Journal of Economic Perspectives, Spring 1993,
159-171.
John McDonald, The Game of Business, Anchor Books, 1977.
III. Cases
A Note on Racing to Acquire Customers (9-803-103), Harvard Business
School, 2003.
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Judo in Action (9-703-454), Harvard Business School, 2003.
Hold or Fold? The War of Attrition (9-794-092), Harvard Business School,
1998. Teaching Note (5-795-166).
Toy Game (9-795-121), Harvard Business School, 1995.
Teaching Note (5-795-172).
Diaper War: Kimberly-Clark vs. Procter & Gamble (A), (92M003), Richard
Ivey School of Business, 2000. Teaching Note (891MOV)
Ready-to-Eat Breakfast Cereal Industry in 1994 (A) (9-795-191), Harvard
Business School, 1997. Teaching Note (5-796-133).
Bitter Competition: The Holland Sweetener Co vs. Nutrasweet, Parts A-G,
(9-794-079, 080, 081, 082, 083, 084, 085), Harvard Business School, 1995.
Teaching Note (5-795-164).
R&D Race (9-190-108), Harvard Business School, 1992.
Teaching Note (5-191-165).
IV. Quips and Quotes
It is a remarkable fact that [business strategies] are played largely in the
mind. Only a small part of the play appears in overt action. Its full scope
and depth lie in the players’ looking backward and forward and running
through their minds their alternative moves and countermoves. (John
McDonald, The Game of Business)
A game is more than a sport, pastime, and amusement. It is also a model of
the real world. (John McDonald, The Game of Business)
Trust everybody but cut the cards.
If you’ve been in a poker game for thirty minutes and you don’t know who
the patsy is, you’re the patsy.
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