KULIAH BESAR GAME THEORY.ppt game theory

game theory

1. INTRODUCTION TO
GAME THEORY
KULIAH BESAR
DOSEN: DR.ASWIN RIVAI

2. GENERAL APPROACH
•Brief History of Game Theory
•Payoff Matrix
•Types of Games
•Basic Strategies
•Evolutionary Concepts
•Limitations and Problems

3. BRIEF HISTORY OF GAME THEORY
•1913 - E. Zermelo provides the first theorem of
game theory; asserts that chess is strictly
determined
•1928 - John von Neumann proves the minimax
theorem
•1944 - John von Neumann & Oskar Morgenstern
write "Theory of Games and Economic Behavior”
•1950-1953 - John Nash describes Nash
equilibrium

16. RATIONALITY
Assumptions:
•humans are rational beings
•humans always seek the best alternative in a set of possible
choices
Why assume rationality?
•narrow down the range of possibilities
•predictability

17. UTILITY THEORY
Utility Theory based on:
•rationality
•maximization of utility
•may not be a linear function of income or
wealth
It is a quantification of a person's preferences with
respect to certain objects.

18. WHAT IS GAME THEORY?
Game theory is a study of how to mathematically determine the best
strategy for given conditions in order to optimize the outcome

19. BASIC CONCEPTS
•Any situation in which individuals must make
strategic choices and in which the final outcome
will depend on what each person chooses to do
can be viewed as a game.
•Game theory models seek to portray complex
strategic situations in a highly simplified setting.
19

20. WHY IS GAME THEORY
IMPORTANT?
•All intelligent beings make decisions all the time.
•AI needs to perform these tasks as a result.
•Helps us to analyze situations more rationally and
formulate an acceptable alternative with respect to
circumstance.
•Useful in modeling strategic decision-making
•Games against opponents
•Games against "nature„
•Provides structured insight into the value of information

21. BASIC CONCEPTS
•All games have three basic elements:
•Players
•Strategies
•Payoffs
•Players can make binding agreements in cooperative games,
but can not in noncooperative games, which are studied in
this chapter.
21

22. PLAYERS
•A player is a decision maker and can be anything from individuals to
entire nations.
•Players have the ability to choose among a set of possible actions.
•Games are often characterized by the fixed number of players.
•Generally, the specific identity of a play is not important to the game.
22

23. STRATEGIES
•A strategy is a course of action available to a player.
•Strategies may be simple or complex.
•In noncooperative games each player is uncertain about
what the other will do since players can not reach
agreements among themselves.
23

24. PAYOFFS
•Payoffs are the final returns to the players at the conclusion
of the game.
•Payoffs are usually measure in utility although sometimes
measure monetarily.
•In general, players are able to rank the payoffs from most
preferred to least preferred.
•Players seek the highest payoff available.
24

25. EQUILIBRIUM CONCEPTS
•In the theory of markets an equilibrium occurred when all
parties to the market had no incentive to change his or her
behavior.
•When strategies are chosen, an equilibrium would also
provide no incentives for the players to alter their behavior
further.
•The most frequently used equilibrium concept is a Nash
equilibrium.
25

26. TYPES OF GAMES
•Sequential vs. Simultaneous
moves
•Single Play vs. Iterated
•Zero vs. non-zero sum
•Perfect vs. Imperfect information
•Cooperative vs. conflict

27. ZERO-SUM GAMES
•The sum of the payoffs remains constant during the
course of the game.
•Two sides in conflict
•Being well informed always helps a player

28. NON-ZERO SUM GAME
•The sum of payoffs is not constant during the
course of game play.
•Players may co-operate or compete
•Being well informed may harm a player.

29. GAMES OF PERFECT
INFORMATION
•The information concerning an opponent’s move is
well known in advance.
•All sequential move games are of this type.

30. IMPERFECT INFORMATION
•Partial or no information concerning the opponent
is given in advance to the player’s decision.
•Imperfect information may be diminished over time
if the same game with the same opponent is to be
repeated.

31. KEY AREA OF INTEREST
•chance
•strategy

32. MATRIX NOTATION
(Column) Player II
Strategy A Strategy B
(Row) Player I
Strategy A (P1, P2) (P1, P2)
Strategy B (P1, P2) (P1, P2)

Notes:Player I's strategy A may be different from Player II's.
P2 can be omitted if zero-sum game

33. Prisoner’s Dilemma &
Other famous games
A sample of other games:
Marriage
Disarmament (my generals are more irrational than yours)

34. Prisoner’s Dilemma
Notes: Higher payoffs (longer sentences) are bad.
Non-cooperative equilibrium  Joint maximum
Institutionalized “solutions” (a la criminal organizations, KSM)
NCE
Jt. max.

35. GAMES OF CONFLICT
•Two sides competing against each other
•Usually caused by complete lack of information
about the opponent or the game
•Characteristic of zero-sum games

36. GAMES OF CO-OPERATION
Players may improve payoff through
•communicating
•forming binding coalitions & agreements
•do not apply to zero-sum games
Prisoner’s Dilemma
with Cooperation

37. PRISONER’S DILEMMA WITH
ITERATION
•Infinite number of iterations
•Fear of retaliation
•Fixed number of iteration
•Domino effect

38. BASIC STRATEGIES
1. Plan ahead and look back
2. Use a dominating strategy if possible
3. Eliminate any dominated strategies
4. Look for any equilibrium
5. Mix up the strategies

39. PLAN AHEAD AND LOOK BACK

40. IF YOU HAVE A DOMINATING
STRATEGY,
USE IT
Use strategy 1

41. ELIMINATE ANY DOMINATED STRATEGY
Eliminate strategy
2 as it’s dominated
by strategy 1

42. LOOK FOR ANY EQUILIBRIUM
•Dominating Equilibrium
•Minimax Equilibrium
•Nash Equilibrium

43. MAXIMIN & MINIMAX
EQUILIBRIUM
•Minimax - to minimize the maximum loss
(defensive)
•Maximin - to maximize the minimum gain
(offensive)
•Minimax = Maximin

44. MAXIMIN & MINIMAX EQUILIBRIUM
STRATEGIES

45. DEFINITION: NASH EQUILIBRIUM
“If there is a set of strategies with the property that
no player can benefit by changing her strategy while
the other players keep their strategies unchanged,
then that set of strategies and the corresponding
payoffs constitute the Nash Equilibrium. “
Source: http://www.lebow.drexel.edu/economics/mccain/game/game.html

46. NASH EQUILIBRIUM
•A Nash equilibrium is a pair of strategies (a*,b*) in a
two-player game such that a* is an optimal strategy for A
against b* and b* is an optimal strategy for B against A*.
•Players can not benefit from knowing the equilibrium strategy of
their opponents.
•Not every game has a Nash equilibrium, and some games
may have several.
46

47. IS THIS A NASH EQUILIBRIUM?

48. AN ILLUSTRATIVE ADVERTISING
GAME
•A makes the first move by choosing either H or L at the
first decision “node.”
•Next, B chooses either H or L, but the large oval
surrounding B’s two decision nodes indicates that B does
not know what choice A made.
48

49. FIGURE 12.1: THE ADVERTISING GAME IN
EXTENSIVE FORM
49
7,5
L
L
H
L
H
H
B
B
A
5,4
6,4
6,3

50. AN ILLUSTRATIVE ADVERTISING
GAME
•The numbers at the end of each branch, measured in
thousand or millions of dollars, are the payoffs.
•For example, if A chooses H and B chooses L, profits will be 6 for
firm A and 4 for firm B.
•The game in normal (tabular) form is shown in Table 12.1
where A’s strategies are the rows and B’s strategies are the
columns.
50

51. TABLE 12.1: THE ADVERTISING GAME
IN NORMAL FORM
51
B’s Strategies
L H
L 7, 5 5, 4
A’s Strategies
H 6, 4 6, 3

52. DOMINANT STRATEGIES AND
NASH EQUILIBRIA
•A dominant strategy is optimal regardless of the strategy adopted by an
opponent.
•As shown in Table 12.1 or Figure 12.1, the dominant strategy for B is L since this
yields a larger payoff regardless of A’s choice.
•If A chooses H, B’s choice of L yields 5, one better than if the choice of H was
made.
•If A chooses L, B’s choice of L yields 4 which is also one better than the choice
of H.
52

53. DOMINANT STRATEGIES AND
NASH EQUILIBRIA
•A will recognize that B has a dominant strategy and choose
the strategy which will yield the highest payoff, given B’s
choice of L.
•A will also choose L since the payoff of 7 is one better than the
payoff from choosing H.
•The strategy choice will be (A: L, B: L) with payoffs of 7 to A
and 5 to B.
53

54. DOMINANT STRATEGIES AND
NASH EQUILIBRIA
•Since A knows B will play L, A’s best play is also L.
•If B knows A will play L, B’s best play is also L.
•Thus, the (A: L, B: L) strategy is a Nash equilibrium: it meets the
symmetry required of the Nash criterion.
•No other strategy is a Nash equilibrium.
54

55. TWO SIMPLE GAMES
•Table 12.2 (a) illustrates the children’s finger game, “Rock,
Scissors, Paper.”
•The zero payoffs along the diagonal show that if players adopt the
same strategy, no payments are made.
•In other cases, the payoffs indicate a $1 payment from the loser to
winner under the usual hierarchy (Rock breaks Scissors, Scissors cut
Paper, Paper covers Rock).
55

56. TABLE 12.2 (A): ROCK, SCISSORS, PAPER--
NO NASH EQUILIBRIA
56
B’s Strategies
Rock Scissors Paper
Rock 0, 0 1, -1 -1, 1
Scissors -1, 1 0, 0 1, -1 A’ Strategies
Paper 1, -1 -1, 1 0, 0

57. TWO SIMPLE GAMES
•This game has no equilibrium.
•Any strategy pair is unstable since it offers at least one of the players an
incentive to adopt another strategy.
•For example, (A: Scissors, B: Scissors) provides and incentive for either A or B to
choose Rock.
•Also, (A: Paper, B: Rock) encourages B to choose Scissors.
57

58. TWO SIMPLE GAMES
•Table 12.2 (b) shows a game where a husband (A) and wife
(B) have different preferences for a vacation (A prefers
mountains, B prefers the seaside)
•However, both players prefer a vacation together (where
both players receive positive utility) than one spent apart
(where neither players receives positive utility).
58

59. TABLE 12.2 (B): BATTLE OF THE
SEXES--TWO NASH EQUILIBRIA
59
B’s Strategies
MountainSeaside
Mountain 7, 5 5, 4
A’s Strategies
Seaside 6, 4 6, 3

60. TWO SIMPLE GAMES
•At the strategy (A: Mountain, B: Mountain), neither player
can gain by knowing the other’s strategy.
•The same is true with the strategy (A: Seaside, B: Seaside).
•Thus, this game has two Nash equilibria.
60

61. APPLICATION 12.1: NASH
EQUILIBRIUM ON THE BEACH
•Applications of the Nash equilibrium concept have been
used to analyze where firms choose to operate.
•The concept can be used to analyze where firm’s locate
geographically.
•The concept can also be used to analyze where firm’s
locate in the spectrum of specific types of products.
61

62. APPLICATION 12.1: NASH
EQUILIBRIUM ON THE BEACH
•Hotelling’s Beach
•Hotelling looked at the pricing of ice cream sellers along a linear
beach.
•If people are evenly spread over the length of the beach, he showed
that each seller had an advantage selling to nearby consumers who
incur lower (walking) costs.
•The Nash equilibrium concept can be used to show the optimal
location for each seller.
62

63. APPLICATION 12.1: NASH
EQUILIBRIUM ON THE BEACH
•Milk Marketing in Japan
•In southern Japan, four local marketing boards regulate the sale of
milk.
•It appears that each must take into account what the other boards
are doing, since milk can be shipped between regions.
•A Nash equilibrium similar to the Cournot model found prices about
30 percent above competitive levels.
63

64. APPLICATION 12.1: NASH
EQUILIBRIUM ON THE BEACH
•Television Scheduling
•Firms can also choose where to locate along the spectrum that
represents consumers’ preferences for characteristics of a product.
•Firms must take into account what other firms are doing, so game
theory applies.
•In television, viewers’ preferences are defined along two dimensions--
program content and broadcast timing.
64

65. APPLICATION 12.1: NASH EQUILIBRIUM
ON THE BEACH
•In general, the Nash equilibrium tended to focus on central locations
•There is much duplication of both program types and schedule
timing
•This has left “room” for specialized cable channels to attract viewers
with special preferences for content or viewing times.
•Sometimes the equilibria tend to be stable (soap operas and
sitcoms) and sometimes unstable (local news programming).
65

66. THE PRISONER’S DILEMMA
•The Prisoner’s Dilemma is a game in which the optimal
outcome for the players is unstable.
•The name comes from the following situation.
•Two people are arrested for a crime.
•The district attorney has little evidence but is anxious to extract a
confession.
66

67. THE PRISONER’S DILEMMA
•The DA separates the suspects and tells each, “If you confess and your
companion doesn’t, I can promise you a six-month sentence, whereas your
companion will get ten years. If you both confess, you will each get a three
year sentence.”
•Each suspect knows that if neither confess, they will be tried for a
lesser crime and will receive two-year sentences.
67

68. THE PRISONER’S DILEMMA
•The normal form of the game is shown in Table 12.3.
•The confess strategy dominates for both players so it is a Nash
equilibria.
•However, an agreement not to confess would reduce their prison
terms by one year each.
•This agreement would appear to be the rational solution.
68

69. TABLE 12.3: THE PRISONER’S
DILEMMA
69
B
ConfessNot confess
Confess
A: 3 years
B: 3 years
A: 6 months
B: 10 years
A
Not confess
A: 10 years
B: 6 months
A: 2 years
B: 2 years

70. THE PRISONER’S DILEMMA
•The “rational” solution is not stable, however, since each
player has an incentive to cheat.
•Hence the dilemma:
•Outcomes that appear to be optimal are not stable and cheating will
usually prevail.
70

72. PRISONER’S DILEMMA
APPLICATIONS
•Table 12.4 contains an illustration in the advertising context.
•The Nash equilibria (A: H, B: H) is unstable since greater profits could be earned if they
mutually agreed to low advertising.
•Similar situations include airlines giving “bonus mileage” or farmers unwilling to restrict
output.
•The inability of cartels to enforce agreements can result in competitive
like outcomes.
72

76. TABLE 12.4: AN ADVERTISING GAME
WITH A DESIRABLE OUTCOME THAT
IS UNSTABLE
76
B’s Strategies
L H
L 7, 7 3, 10
A’s Strategies
H 10, 3 5, 5

77. COOPERATION AND REPETITION
•In the version of the advertising game shown in Table 12.5,
the adoption of strategy H by firm A has disastrous
consequences for B (-50 if L is chosen, -25 if H is chosen).
•Without communication, the Nash equilibrium is (A: H, B:
H) which results in profits of +15 for A and +10 for B.
77

78. TABLE 12.5: A THREAT GAME IN
ADVERTISING
78
B’s Strategies
L H
L 20, 5 15, 10
A’s Strategies
H 10, -50 5, -25

79. COOPERATION AND REPETITION
•However, A might threaten to use strategy H unless B plays L to
increase profits by 5.
•If a game is replayed many times, cooperative behavior my be fostered.
•Some market are thought to be characterized by “tacit collusion” although firms
never meet.
•Repetition of the threat game might provide A with the opportunity to
punish B for failing to choose L.
79

80. MANY-PERIOD GAMES
•Figure 12.2 repeats the advertising game except that B
knows which advertising spending level A has chosen.
•The oral around B’s nodes has been eliminated.
•B’s strategic choices now must be phrased in a way that
takes the added information into account.
80

81. FIGURE 12.2: THE ADVERTISING GAME IN
SEQUENTIAL FORM
81
7,5
L
L
H
L
H
H B
B
A
5,4
6,4
6,3

82. MANY-PERIOD GAMES
•The four strategies for B are shown in Table 12.6.
•For example, the strategy (H, L) indicates that B chooses L if A first
chooses H.
•The explicit considerations of contingent strategy choices
enables the exploration of equilibrium notions in dynamic
games.
82

83. TABLE 12.6: CONTINGENT STRATEGIES
IN THE ADVERTISING GAME
83
B’s Strategies
L, L L, H H, L H, H
L 7, 5 7, 5 5, 4 5, 4
A’s Strategies
H 6, 4 6, 3 6, 4 6, 3

84. CREDIBLE THREAT
•The three Nash equilibria in the game shown in Table 12.6
are:
•(1) A: L, B: (L, L);
•(2) A: L, B: (L, H); and
•(3) A: H, B: (H,L).
•Pairs (2) and (3) are implausible, however, because they
incorporate a noncredible threat that firm B would never
carry out.
84

85. CREDIBLE THREAT
•Consider, for example, A: L, B: (L, H) where B promises to
play H if A plays H.
•This threat is not credible (empty threats) since, if A has chosen H, B
would receive profits of 3 if it chooses H but profits of 4 if it chooses
L.
•By eliminating strategies that involve noncredible threats, A
can conclude that, as before, B would always play L.
85

86. CREDIBLE THREAT
•The equilibrium A: L, B: (L, L) is the only one that does not involve
noncredible threats.
•A perfect equilibrium is a Nash equilibrium in which the strategy
choices of each player avoid noncredible threats.
•That is, no strategy in such an equilibrium requires a player to carry out an action that
would not be in its interest at the time.
86

87. MODELS OF PRICING BEHAVIOR:
THE BERTRAND EQUILIBRIUM
•Assume two firms (A and B) each producing a
homogeneous good at constant marginal cost, c.
•The demand is such that all sales go to the firm with the
lowest price, and sales are evenly split if P
A
= P
B
.
•All prices where profits are nonnegative, (P  c) are in
each firm’s pricing strategy.
87

88. THE BERTRAND EQUILIBRIUM
•The only Nash equilibrium is P
A = P
B = c.
•Even with only two firms, the Nash equilibrium is the competitive equilibrium where
price equals marginal cost.
•To see why, suppose A chooses P
A
> c.
•B can choose P
B
< P
A
and capture the market.
•But, A would have an incentive to set P
A
< P
B
.
•This would only stop when P
A
= P
B
= c.
88

89. TWO-STAGE PRICE GAMES AND
COURNOT EQUILIBRIUM
•If firms do not have equal costs or they do not produce
goods that are perfect substitutes, the competitive
equilibrium is not obtained.
•Assume that each firm first choose a certain capacity
output level for which marginal costs are constant up to
that level and infinite thereafter.
89

90. TWO-STAGE PRICE GAMES AND
COURNOT EQUILIBRIUM
•A two-stage game where the firms choose capacity first
and then price is formally identical to the Cournot analysis.
•The quantities chosen in the Cournot equilibrium represent a Nash
equilibrium, and the only price that can prevail is that for which total
quantity demanded equals the combined capacities of the two firms.
90

91. TWO-STAGE PRICE GAMES AND
COURNOT EQUILIBRIUM
•Suppose Cournot capacities are given by
•
•A situation in which is not a Nash
equilibrium since total quantity demanded exceeds capacity.
•Firm A could increase profits by slightly raising price and still selling
its total output.
91
price.capacity full the is P that and q and q
BA
PPP
BA


92. TWO-STAGE PRICE GAMES AND
COURNOT EQUILIBRIUM
PPP
BA

 Similarly,
•is not a Nash equilibrium because at least one firm is selling
less than its capacity.
•The only Nash equilibrium is which is
indistinguishable from the Cournot result.
•This price will be less than the monopoly price, but will exceed
marginal cost.
92
,PPP
BA 

93. COMPARING THE BERTRAND AND
COURNOT RESULTS
•The Bertrand model predicts competitive outcomes in a
duopoly situation.
•The Cournot model predict monopolylike inefficiencies in
which price exceed marginal cost.
•The two-stage model suggests that decisions made prior to
the final (price setting) stage can have important market
impact.
93

94. APPLICATION 12.2: HOW IS THE PRICE
GAME PLAYED?
•Many factors influence how the pricing “game” is played in imperfectly
competitive industries.
•Two such factors that have been examined are
•Product Availability
•Information Sharing
94

95. APPLICATION 12.2: HOW IS THE
PRICE GAME PLAYED?
•Product availability is an important component of
competition in many retail industries.
•The impact of movie availability in the video-rental industry
was examined in 2001 by James Dana.
•His data showed that Blockbuster’s prices were 40% higher
than at other stores.
•He argued that Blockbuster’s higher price in part stems
from its reputation for having movies available and that
those prices act as a signal.
95

96. APPLICATION 12.2: HOW IS THE
PRICE GAME PLAYED?
•Firms in the same industry often share information
with each other at many levels.
•A 2000 study of cross-shareholding in the Dutch
financial sector showed clear evidence that
competition was reduced when firms had financial
interests in each other’s profits.
•A famous 1914 antitrust case found that a price list
published by lumber retailers facilitated higher prices
by discouraging wholesalers from selling at retail.
96

97. TACIT COLLUSION: FINITE TIME
HORIZON
•Would the single-period Nash equilibrium in the Bertrand
model, P
A = P
B = c, change if the game were repeated
during many periods?
•With a finite period, any strategy in which firm A, say, chooses, P
A
> c
in the last period offers B the possibility of earning profits by setting
P
A
> P
B
> c.
97

98. TACIT COLLUSION: FINITE TIME
HORIZON
•The threat of charging P
A
> c in the last period is not credible.
•A similar argument is applicable for any period before the last period.
•The only perfect equilibrium requires firms charge the
competitive price in all periods.
•Tacit collusion is impossible over a finite period.
98

99. TACIT COLLUSION: INFINITE TIME
HORIZON
•Without a “final” period, there may exist collusive
strategies.
•One possibility is a “trigger” strategy where each firm sets its price
at the monopoly price so long as the other firm adopts a similar
price.
•If one firm sets a lower price in any period, the other firm sets
its price equal to marginal cost in the subsequent period.
99

100. TACIT COLLUSION: INFINITE TIME
HORIZON
•Suppose the firms collude for a time and firm A considers
cheating in this period.
•Firm B will set P
B
= P
M
(the cartel price)
•A can set its price slightly lower and capture the entire market.
•Firm A will earn (almost) the entire monopoly profit (
M
) in this
period.
100

101. TACIT COLLUSION: INFINITE TIME
HORIZON
•Since the present value of the lost profits is given by
(where r is the per period interest rate)
•This condition holds for values of r < ½.
•Trigger strategies constitute a perfect equilibrium for
sufficiently low interest rates.
.
1
2
if profitable be willcheating
,
1
2























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r
r
M
M
M


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10
1

102. GENERALIZATIONS AND
LIMITATIONS
•Assumptions of the tacit collusion model:
•Firm B can easily detect whether firm A has cheated
•Firm B responds to cheating by adopting a harsh response that
punishes firm A, and condemns itself to zero profit forever.
•More general models relax one or both of these
assumptions with varying results.
102

103. APPLICATION 12.3: THE GREAT
ELECTRICAL EQUIPMENT CONSPIRACY
•Manufacturing of electric turbine generators and high
voltage switching units provided a very lucrative business to
such major producers and General Electric, Westinghouse,
and Federal Pacific Corporations after World War II.
•However, the prospect of possible monopoly profits proved
enticing.
103

104. APPLICATION 12.3: THE GREAT
ELECTRICAL EQUIPMENT CONSPIRACY
•To collude they had to create a method to coordinate their
sealed bids.
•This was accomplished through dividing the country into bidding
regions and using the lunar calendar to decide who would “win” a
bid.
•The conspiracy became more difficult as its leaders had to
give greater shares to other firms toward the end of the
1950s.
104

105. APPLICATION 12.3: THE GREAT
ELECTRICAL EQUIPMENT CONSPIRACY
•The conspiracy was exposed when a newspaper reporter
discovered that some of the bids on Tennessee Valley
Authority projects were similar.
•Federal indictments of 52 executives lead to jail time for
some and resulted in a chilling effect on the future
establishment of other cartels of this type.
105

106. ENTRY, EXIT, AND STRATEGY
•Sunk Costs
•Expenditures that once made cannot be recovered include
expenditures on unique types of equipment or job-specific training.
•These costs are incurred only once as part of the entry process.
•Such entry investments mean the firm has a commitment to the
market.
106

107. FIRST-MOVER ADVANTAGES
•The commitment of the first firm into a market may limit
the kinds of actions rivals find profitable.
•Using the Cournot model of water springs, suppose firm A
can move first.
•It will take into consideration what firm B will do to maximize profits
given what firm A has already done.
107

108. FIRST-MOVER ADVANTAGES
•Firm A knows fir B’s reaction function which it can use to
find its profit maximizing level of output.
•Using the previously discussed functions.
.2120
gives qfor Solving
.
2
60
2
)120(
120120
2
120
A
Pq
P
q
P
q
Pqq
q
q
A
A
A
BA
A
B






10
8

109. FIRST-MOVER ADVANTAGES
•Marginal revenue equals zero (revenue andprofits are maximized)
when q
A
= 60.
•With firm A’s choice, firm B chooses to produce
•Market output equals 90 so spring water sells for $30 increasing A’s
revenue by $200 to $1800.
•Firm B’s revenue falls by $700 to $900.
•This is often called a “Stakelberg equilibrium.”
.30
2
)60120(
2
120





A
B
q
q
10
9

110. ENTRY DETERRENCE
•In the previous model, firm A could only deter firm B from
entering the market if it produces the full market output of
120 units yielding zero revenue (since P = $0).
•With economies of scale, however, it may be possible for a
first-mover to limit the scale of operation of a potential
entrant and deter all entry into the market.
110

111. A NUMERICAL EXAMPLE
•One simple way to incorporate economies of scale is to
have fixed costs.
•Using the previous model, assume each firm has to pay
fixed cost of $784.
•If firm A produced 60, firm B would earn profits of $116 (= $900 -
$784) per period.
•If firm A produced 64, firm B would choose to produce 28 [ = (120-
64)  2].
111

112. A NUMERICAL EXAMPLE
•Total output would equal 92 with P = $28.
•Firm B’s profits equal zero [profits = TR - TC = ($28·28) - $784 = 0] so it would not
enter.
•Firm A would choose a price of $56 (= 120 - 64) and earn profits of $2,800 [=
($56·64) - $784].
•Economies of scale along with the chance to be the first mover yield a
profitable entry deterrence.
112

113. APPLICATION 12.4: FIRST-MOVER ADVANTAGES FOR ALCOA,
DUPONT, PROCTER AND GAMBLE, AND WAL-MART
•Consider two types of first-mover advantages
•Advantages that stem from economies of scale in production.
•Advantages that arise in connection with the introduction of
pioneering brands.
113

114. APPLICATION 12.4: FIRST-MOVER ADVANTAGES FOR ALCOA,
DUPONT, PROCTER AND GAMBLE, AND WAL-MART
•Economies of Scale for Alcoa and DuPont.
•The first firm in the market may “overbuild” its initial plant to realize
economies of scale when the demand for the product expands.
•Antitrust action against the Aluminum Company of America (Alcoa)
claimed that it built larger plants than justified by current demand.
114

115. LIMIT PRICING
•A limit price is a situation where a monopoly might purposely
choose a low (“limit”) price policy with a goal of deterring entry
into its market.
•If an incumbent monopoly chooses a price P
L < P
M (the profit-maximizing
price) it is hurting its current profits.
•P
L will deter entry only if it falls short of the average cost of a potential
entrant.
115

116. LIMIT PRICING
•If the monopoly and potential entrant have the same
costs (and there are no capacity constraints), the only
limit price is P
L
= AC, which results in zero economic
profits.
•Hence, the basic monopoly model does not provide a
mechanism for limit pricing to work.
•Thus, a limit price model must depart from traditional
assumptions.
116

117. INCOMPLETE INFORMATION
•If an incumbent monopoly knows more about the market
than a potential entrant, it may be able to use this
knowledge to deter entry.
•Consider Figure 12.3.
•Firm A, the incumbent monopolist, may have “high” or
“low” production costs based on past decisions which
are unknown to firm B.
117

118. FIGURE 12.3: AN ENTRY GAME118
1,3
Entry
High cost
No entry
Entry
No entry
Low cost
B
B
A
4,0
3, -1
6,0

119. INCOMPLETE INFORMATION
•Firm B, the potential entrant, must consider both
possibilities since this affects its profitability.
•If A’s costs are high, B’s entry is profitable (
B = 3).
•If A’s costs are low, B’s entry is unprofitable
(
B = -1).
•Firm A is clearly better off if B does not enter.
•A low-price policy might signal that firm A is low cost
which could forestall B’s entry.
119

120. PREDATORY PRICING
•The structure of many predatory pricing models also stress
asymmetric information.
•An incumbent firm wishes its rival would exit the market so it takes
actions to affect the rival’s view of future profitability.
•As with limit pricing, the success depends on the ability of the
monopoly to take advantage of its better information.
120

121. PREDATORY PRICING
•Possible strategies include:
•Signal low costs with a low-price policy.
•Adopt extensive production differentiation to indicate the existence
of economies of scale.
•Once a rival is convinced the incumbent firm possess an
advantage, it may exit the market, and the incumbent gains
monopoly profits.
121

122. APPLICATION 12.4: THE STANDARD OIL
LEGEND
•The Standard Oil case of 1911 was one of the
landmarks of U.S. antitrust law.
•In that case, Standard Oil Company was found to have
“attempted to monopolize” the production, refining,
and distribution of petroleum in the U.S., violating the
Sherman Act.
•The government claimed that the company would cut
prices dramatically to drive rivals out of a particular
market and then raise prices back to monopoly levels.
122

123. APPLICATION 12.4: THE STANDARD OIL
LEGEND
•Unfortunately, the notion that Standard Oil
practiced predatory pricing policies in order to
discourage entry and encourage exit by its rivals
makes little sense in terms of economic theory.
•Actually, the predator would have to operate
with relatively large losses for some time in the
hope that the smaller losses this may cause rivals
will eventually prompt them to give it up.
•This strategy is clearly inferior to the strategy of
simply buying smaller rivals in the marketplace.
123

124. APPLICATION 12.4: THE STANDARD OIL
LEGEND
•In a famous 1958 article, J.S. McGee concluded that
Standard Oil neither trieds to use predatory policies nor
did its actual price policies have the effect of driving rivals
from the oil business.
•McGee examined over 100 refineries bought by Standard
Oil and found no evidence that predatory behavior by
Standard Oil caused these firms to sell out.
•Indeed, in many cases Standard Oil paid quite good prices
for these refineries.
124

125. N-PLAYER GAME THEORY
•The most important additional element added when the
game goes beyond two players is the possibility for the
formation of subsets of players.
•Coalitions are combinations of two or more players in a
game who adopt coordinated strategies.
•A two-person game example is a cartel.
125

126. N-PLAYER GAME THEORY
•The formation of successful coalitions in n-player games if
influenced by organizational costs.
•Information costs associated with determining coalition strategies.
•Enforcement costs associated with ensuring that a coalition’s chosen
strategy is actually followed by its members.
126

127. WHERE IS GAME THEORY
CURRENTLY USED?
–Ecology
–Networks
–Economics

128. LIMITATIONS & PROBLEMS
•Assumes players always maximize their outcomes
•Some outcomes are difficult to provide a utility for
•Not all of the payoffs can be quantified
•Not applicable to all problems

130. SUMMARY
•What is game theory?
•Abstraction modeling multi-person interactions
•How is game theory applied?
•Payoff matrix contains each person’s utilities for
various strategies
•Who uses game theory?
•Economists, Ecologists, Network people,...
•How is this related to AI?
•Provides a method to simulate a thinking agent

131. SOURCES
•Much more available on the web.
•These slides (with changes and additions) adapted from:
http://pages.cpsc.ucalgary.ca/~jacob/Courses/Winter2000/CPSC533/Pages/index.html
•Three interesting classics:
•John von Neumann & Oskar Morgenstern, Theory of Games &
Economic Behavior (Princeton, 1944).
•John McDonald, Strategy in Poker, Business & War (Norton,
1950)
•Oskar Morgenstern, "The Theory of Games," Scientific
American, May 1949; translated as "Theorie des Spiels," Die
Amerikanische Rundschau, August 1949.