1

Lecture 7Rivalry, Strategic Behavior and

Game Theory

Overview

Game TheorySimultaneous-move, nonrepeated

interactionSequential interactionsRepeated strategic interactionsPricing coordination

2

Introduction

So far we have used fairly static, simplistic models to study firms’ strategic interactionsWant to begin developing tools that will

allow us to analyze more complex interactions– When firms interact repeatedly over multiple

periodLeads to more realistic outcomes

3

Game Theory

To analyze manager’s strategic interactions in the market we use something called Game Theory. One way economists use game theory is

to address the question: “If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions?”

4

Game Theory

Game Theory has been applied in a number of different areas by social scientists.Originally developed to analyze

interactions of countries, with emphasis on the Cold War and Nuclear deterrence.Also used by Political Scientists to model

the behavior of legislative bodies and why people vote.

5

Game Theory: Payoff interdependency??? Decision-theoretic vs. Game-theoretic Situations

o Local Water Co. is contemplating raising local water prices to cover costs of upgrading its infrastructure.

o Google contemplates changing the price it charges for “clicks”.o Raywood Stelly contemplates price and output for the upcoming harvest season.o KFC in downtown Athens contemplates changing the hourly wage it pays to new

employees.o Apple contemplates the features it makes standard on its new iPhone.o Honda contemplates offering a $2000 rebate on new Accords to reduce inventories on

dealer lots.o UPS contemplates offering weekend delivery at the same rate as weekday delivery.o American Airlines contemplates raising the price of its non-stop flight from New York to

Paris. With some situations the optimal strategy for a firm to pursue depends only

on the market circumstances and environment in which the firm finds itself. The behavior or reactions of other parties are not a factor. There is no Payoff Interdependency.

In other situations a firm’s optimal strategy will depend on the actions or reactions taken by other parties. There is Payoff Interdependency. This payoff interdependency puts us in the realm of Game Theory.

Elements of a game, Types of games

Elements of a game: Players Rules: timing of moves, actions available to players on each

move, information available to players when they make a move Outcomes Payoffs associated with each possible outcome

Types of games: Static: players move simultaneously. Examples?

https://www.youtube.com/watch?v=ui-mzTCmZPEhttps://www.youtube.com/watch?v=g6tR78d0cmA

Dynamic: players move sequentially. Examples?https://www.youtube.com/watch?v=GL-uWmw4YMA.

Information available: we will restrict our analysis to games where all players have complete information about players, rules, outcomes, and payoffs.

Game Theory

Characteristics of Games1. There are two or more players

• Games with one player are boring.2. Each player maximizes her utility, called a

payoff• What we have been assuming all along.

8

Game Theory

Characteristics of Games3. Each player knows the other players actions

can affect her payoff. • No need to consider interactions if this is not

true.4. The other player’s interests are neither

perfectly opposed nor perfectly coincident with those of a given player. • Must be some room for both gains from

cooperation and competition.

9

Game Theory

There are two main type of games, Cooperative Games and Noncooperative Games.

10

Game Theory

Noncooperative versus Cooperative Games– Cooperative Game

• Players negotiate binding contracts that allow them to plan joint strategies

– Example: Buyer and seller negotiating the price of a good or service or a joint venture by two firms (i.e. Microsoft and Apple)

– Binding contracts are possible

11

Game Theory

Noncooperative versus Cooperative Games– Noncooperative Game

• Negotiation and enforcement of a binding contract are not possible

– Example: Two competing firms take each other’s likely behavior into account when independently setting pricing and advertising strategy to gain market share

12

Cooperative vs. non-cooperative games If players are able to enter into binding commitments

to pursue strategies that are not in their narrow self-interest, then they will be able to collude. We call such games cooperative.

If players cannot make binding commitments, they cannot be counted on to honor any agreements that are not incentive compatible. We call this type of game non-cooperative.

http://www.youtube.com/watch?v=zpahL4fu5R8 https://www.youtube.com/watch?v=S0qjK3TWZE8 Are contracts to collude legally enforceable in the

Greece/EU? https://en.wikipedia.org/wiki/Article_101_of_the_Treaty_on_the_Functioning_of_the_European_Union

An example in game theory, called the Prisoners’ Dilemma, illustrates the problem oligopolistic firms face.

Competition Versus Collusion:The Prisoners’ Dilemma

14

Scenario– Two prisoners have been accused of

collaborating in a crime.– They are in separate jail cells and cannot

communicate.– Each has been asked to confess to the crime.

Competition Versus Collusion:The Prisoners’ Dilemma

16

-5, -5 -1, -10

-2, -2-10, -1

Payoff Matrix for Prisoners’ Dilemma

Prisoner A

Confess Don’t confess

Confess

Don’tconfess

Prisoner B

Would you choose to confess?

17

Strategies

Before figuring out what players will do we have to talk about their strategies. A firm’s strategy is based on

understanding your opponent’s point of view, and (assuming you opponent is rational) deducing how he or she is likely to respond to your actions.

18

Solution strategies

Dominant strategy: a strategy that maximizes a player’s payoffs regardless of the strategy chosen by the other player.

Iterative elimination of dominated strategies: a dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy.

Rationalizable strategies: a rational player will not play a strategy that is never a best response to any strategy the other player might choose.

Nash equilibrium: a strategy profile such that each player’s chosen strategy is a best response to the strategy selected by the other player. Neither player will experience ex-post regret.

Dominant Strategies

Dominant Strategy

– One that is optimal no matter what an opponent does.

Back to Prisoner’s Dilemma game. Is their a dominant strategy here and if so, what is it?

20

-5, -5 -1, -10

-2, -2-10, -1

Payoff Matrix for Prisoners’ Dilemma

Prisoner A

Confess Don’t confess

Confess

Don’tconfess

Prisoner B

Would you choose to confess?

21

Pricing Game

Let’s go over a second example.

– A & B sell competing products

– They are deciding whether to undertake advertising campaigns

22

Payoff Matrix for Advertising Game

Firm A

AdvertiseDon’t

Advertise

Advertise

Don’tAdvertise

Firm B

10, 5 15, 0

10, 26, 8

23

Payoff Matrix for Advertising Game

Firm A

AdvertiseDon’t

Advertise

Advertise

Don’tAdvertise

Firm B

10, 5 15, 0

10, 26, 8

Observations– A: regardless of

B, advertising is the best

– B: regardless of A, advertising is best

24

Payoff Matrix for Advertising Game

Firm A

AdvertiseDon’t

Advertise

Advertise

Don’tAdvertise

Firm B

10, 5 15, 0

10, 26, 8

Observations– Dominant

strategy for A & Bis to advertise

– Do not worry about the other player

– Equilibrium is dominant strategy

25

Dominant Strategies

Game Without Dominant Strategy

– The optimal decision of a player without a dominant strategy will depend on what the other player does.

26

10, 5 15, 0

20, 26, 8

Firm A

AdvertiseDon’t

Advertise

Advertise

Don’tAdvertise

Firm B

Modified Advertising Game

27

10, 5 15, 0

20, 26, 8

Firm A

AdvertiseDon’t

Advertise

Advertise

Don’tAdvertise

Firm B

Modified Advertising Game

Observations– A: No dominant

strategy; depends on B’s actions

– B: AdvertiseQuestion

– What should A do? (Hint: consider B’sdecision

28

The Nash Equilibrium Revisited

Dominant Strategies– “I’m doing the best I can no matter what you

do.”– “You’re doing the best you can no matter what

I do.”

29

The Nash Equilibrium Revisited

Nash Equilibrium– “I’m doing the best I can given what you are

doing”– “You’re doing the best you can given what I

am doing.”

30

Implications

If a Nash equilibrium exists then it is self-enforcing—no firm has an incentive to deviate from the strategy– Can be multiple Nash equilibria

Firms have an even stronger incentive to choose a dominant strategy if one exists; in this situation you can be fairly certain how your rival will behave

31

Implications

More likely to reach a Nash equilibrium when– Firms have experience in similar situations– Firms are better informed– There is a natural focal point

32

Iterative elimination of dominated strategies Now we are ready to explore ways of solving for the

outcome of games of strategy. The first thing to do is to look for dominant strategies. If a player has a dominant strategy, she will play it.

The second thing to do, if there is no dominant strategy, is to look for dominated strategies and eliminate them from consideration. A dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy. A rational player would never choose to play a dominated strategy.

Dominated Strategies

Hilton and Hyatt are both considering building a hotel on an islandThree possible choices, 70, 80, or 90 beds

34

Dominated Strategies

$36, $36 $30, $40 $18, $36

$40, $30 $32, $32 $16, $24

$36, $18 $24, $16 $10, $10

35

70 Beds 80 Beds 90 Beds

70 Beds

80 Beds

90 Beds

Hilton

Hyatt

Dominated Strategies

Hyatt would never build a 90 bed hotel because they always get a higher payoff with the 80 bed hotelHilton would never build a 90 bed hotel

because they always get a higher payoff with a 80 bed hotelOnce we eliminate this choice we are back

to the simpler 2x2 matrix

36

Iterative elimination of dominated strategies Now we are ready to explore ways of solving for the

outcome of games of strategy. The first thing to do is to look for dominant strategies. If a player has a dominant strategy, she will play it.

The second thing to do, if there is no dominant strategy, is to look for dominated strategies and eliminate them from consideration. A dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy. A rational player would never choose to play a dominated strategy.

Can you predict the outcome of this game?

Does either player have a dominant strategy? Are there any dominated strategies for either player?

Predicted outcome: R1, C1. Note that the level of complexity went up one notch. The column player has to get inside the row player’s head and understand how he will think in order to determine what strategy is best for her.

Column PlayerC1 C2 C3

Row R1 4, 3 5, 1 6, 2Player R2 2, 1 3, 4 3, 6

R3 3, 0 9, 6 2, 8

Rationalizable Strategies

How would you solve this game?

Are there any dominant strategies? Are there any dominated strategies?

Another solution concept: a strategy is a best response for player i when player j plays a certain strategy if player i’s strategy choice yields the highest possible payoff among her set of choices.

A rational player will not play a strategy that is never a best response.

Column PlayerLeft Middle Right

Row Up 2, 0 3, 5 4, 4Player Down 0, 3 2, 1 5, 2

Solution to the previous game

Row player: U is the best response to L or M, and D is the best response to R.

Column player: L is the best response to D, and M is the best response to U.

So R is never a best response for the column player. The row player should not expect that strategy to be played if the column player is rational. That being the case, the row player should not play the D strategy, but should always play the U strategy. And if the row player plays U, then the best response of the column player is to play M.

Not that we have added another layer of complexity. The column player reasons that the row player is reasoning that he will never choose R, and so as a result will have a dominant strategy of U which she will play. The column player’s choice of M is wise only if he can count on the row player having “gotten inside” of his head.

Nash equilibrium

Let’s try a more complicated example:Column Player

C1 C2 C3 C4

Row R1 0, 5 2, 5 7, 0 6, 6

Player R2 5, 2 3, 3 5, 2 2, 2

R3 7, 0 2, 5 0, 7 4, 4

R4 6, 6 2, 2 4, 4 10, 3

Solution to the previous game

Does either player have a dominant strategy? Are there any dominated strategies? Non-rationalizable strategies? So how do we think the game will turn out?

An even stronger solution concept: Nash Equilibrium A Nash equilibrium is a strategy profile such that each

player’s chosen strategy is a best response to the strategy selected by the other player.

In other words, if my strategy choice is the best possible response to your strategy, and at the same time your strategy is the best possible response to my strategy, then this strategy pair is a Nash equilibrium. If that is true, then neither of us will experience ex post regret.

In the previous game, the strategy pair R2, C2 is a Nash equilibrium.

Implications

Managers often make decisions where the situations is not likely to be repeated or not repeated very often– Pricing a new product– Entering a new market– Acquiring another firm

43

Implications

Steps to follow in this situation1. Estimate the payoff of each potential action,

as well as the payoff of your rival2. See if there are any weakly dominate

strategies you can eliminate3. Is there a dominant strategy? If yes, then

take that action4. If no, then estimate what your rival will do

and identify your best action (which may be a mixed strategy)

44

Implications

Steps to follow in this situation5. Check whether the outcome is a Nash

equilibrium6. Check whether the outcome is a Nash

equilibrium—are you forecasting that your rival is behaving optimally? If no, then revise your forecast

Assume your rival is doing the same thing

– Put yourself in their desk45

Implications

If you are risk adverse or have little experience in this situation, may want to consider a secure strategy

– Strategy that minimizes losses– Not the best strategy for the long-run– May be learning-by-doing

46

Prisoner’s dilemma in a business setting http://www.llbean.com/llb/shop/32937?page=warm-up-jacket-fleece-lined http://www.landsend.com/products/mens-classic-squall-

jacket/id_287454_59?cm_mmc=139971612&source=GS&003=56492216&010=4283286&gclid=CNDHivyegM4CFQMQaQodZjcMXQ

Duopolists choosing a pricing strategy:

Does this outcome seem counter-intuitive to you? See: “Resolving the Prisoner’s Dilemma,” (Chapter 4 in Dixit and Nalebuff)

Land’s End

High price: $89.99 Low price: $69.99

L. L. Bean High price: $89.99 πLLB = 100πLE = 100

πLLB = 40πLE = 140

Low price: $69.99 πLLB = 140πLE = 40

πLLB = 60πLE = 60

Implications of the Prisoners’Dilemma for Oligipolistic Pricing

Observations of Oligopoly Behavior

1) In some oligopoly markets, pricing behavior over time can create a predictable pricing environment and implicit collusion may occur.

48

Observations of Oligopoly Behavior

2) In other oligopoly markets, the firms are very aggressive and collusion is not possible. • Firms are reluctant to change price because of the

likely response of their competitors.• In this case prices tend to be relatively rigid.

Implications of the Prisoners’Dilemma for Oligipolistic Pricing

49

Dynamic Price Competition

Price competition can be viewed as a dynamic processDecisions by a firm today will affect its

behavior as well as its competitors’ in the futureDynamic competition can also occur in non-

price dimensions such as quality

50

Dynamic versus Static Models

Dynamic models can address questions that static models cannot (Example: What determines the intensity of price competition?)What appears as short term profits (in a

static model) are often followed by long term negative effects (in a dynamic model)How might Golden Ball outcome change if

they played the game a number of times?51

Dynamic Model Scenarios

Static models cannot explain how firms can maintain prices above competitive levels without formal collusionIn other situations, even a small number of

firms are sufficient to produce intense price competitionDynamic models are useful in exploring

such situations

52

Implications of the Prisoners’ Dilemma for Oligopolistic Pricing

Price Signaling

– Implicit collusion in which a firm announces a price increase in the hope that other firms will follow suit

Price Signaling & Price Leadership

53

Implications of the Prisoners’ Dilemma for Oligopolistic Pricing

Price Leadership

– Pattern of pricing in which one firm regularly announces price changes that other firms then match

Price Signaling & Price Leadership

54

Implications of the Prisoners’ Dilemma for Oligopolistic Pricing

The Dominant Firm (Stackelberg) Model– In some oligopolistic markets, one large firm

has a major share of total sales, and a group of smaller firms supplies the remainder of the market.

– The large firm might then act as the dominant firm, setting a price that maximized its own profits.

55

Tit-for-Tat Pricing

When two firms compete over several periods, a tit-for-tat strategy may make cooperative pricing possibleSince each firm knows that its rival will

match any price cut, neither has an incentive to engage in price cutting

56

Pricing Problem

Firm 1

Low Price High Price

Low Price

High Price

Firm 2

10, 10 100, -50

50, 50-50, 100

57

Pricing Problem

Firm 1

Low Price High Price

Low Price

High Price

Firm 2

10, 10 100, -50

50, 50-50, 100

Non-repeated game– Strategy is Low1,

Low2

Repeated game– Tit-for-tat

strategy is the most profitable

58

Tit-for-Tat Pricing with Many Firms

Condition for sustainable cooperative pricing

N = Number of firms ΠM = Monopoly profit for the industryi = Discount rate Π0 = Prevailing profit for the industry

59

Tit-for-Tat Pricing with Many Firms

The numerator is the annuity a firm will receive by cooperatingThe denominator is the one time gain by not

cooperating and inviting a tit-for-tat response from the rivalsWhen the condition is met, the present

value of the annuity exceeds the one time gain from refusal to cooperate

60

Coordination Problem

While cooperative pricing is sustainable, the folk theorem does not rule out other equilibriaAchieving a desirable equilibrium out of

many possible equilibria is a coordination problemA cooperation inducing strategy that is also

a compelling choice is a focal point

61

Coordination in Practice

Round number price points will help with coordinationEven splits of the market (or status quo for

market shares) is likely to be durable Coordination easier with fewer products that

are identical

62

Coordination in Practice

Conventions and traditions make rivals’ intentions transparent and help with coordination

Examples: Standard cycles for adjusting prices, using standard price points for price quotes

63

Market Structure & Cooperative Pricing

Achieving cooperative pricing may depend on certain market structure conditionsSome examples are:

– Concentration– Conditions that affect reaction speeds and

detection lags– Asymmetries among firms– Price sensitivity of buyers

64

Relevant Structural Conditions

Lumpiness of ordersInformation availability regarding sales

transactionVolatility of demand conditions

65

Practices that Facilitate Cooperative Pricing

Firms can facilitate cooperative pricing by– Price leadership– Advance announcement of price changes– Most favored customer clauses– Uniform delivered pricing

66

67

Cooperative Pricing

Conclusion– Cooperation is difficult at best since these

factors may change in the long-run.

68

Sequential Games

Players move in turn

Players must think through the possible actions and rational reactions of each player

69

Sequential Games

Examples– Responding to a competitor’s ad campaign– Entry decisions– Responding to regulatory policy

70

Scenario– Two new (sweet, crispy) cereals– Successful only if each firm produces one

cereal– Sweet will sell better– Both still profitable with only one producer

Sequential Games

The Extensive Form of a Game

71

Modified Product Choice Problem

Firm 1

Crispy Sweet

Crispy

Sweet

Firm 2

-5, -5 10, 20

-5, -520, 10

72

Modified Product Choice Problem

Firm 1

Crispy Sweet

Crispy

Sweet

Firm 2

-5, -5 10, 20

-5, -520, 10

Question– What is the

likely outcome if both make their decisions independently, simultaneously, and without knowledge of the other’s intentions?

Dynamic Games of Complete Information Now we turn to game theoretic situations where there can

be a sequence of moves and where players may move more than once.

We define a dynamic game by its extensive form, which specifies: The identity and number of players When each player can make a move The choices or options available on each move The information available when making a move The payoffs over all possible outcomes of the game

The extensive form of a dynamic game can be represented by a game tree, which has: Decision nodes Branches: actions available Terminal nodes: payoffs

1

2

2

U

D

u

d

u

d

5, 2

1, 0

4, 4

6, 0

Example of a game tree:

Solving the previous game

Player #1 moves first and has two options, UP or DOWN. If player #1 plays UP, then player #2 moves next. He has

two options, up or down. If player #1 plays DOWN, then player #2 moves next. He has two options, up or down.

If player #1 plays U and player #2 then plays u, the payoff to player #1 is 5 and the payoff to player #2 is 2. U and dresults in payoffs of 1 and 0 to players #1 and #2. D and uresults in payoffs of 4 and 4. D and d results in payoffs of 6 and 0.

How would player #1 want this game to turn out? How would player #2 want the game to turn out? How is the game likely to turn out? Why?

Solving the previous game (continued)

If you are player #1, which strategy do you play? Why?UP, since your likely payoff from UP is 5 while your

likely payoff from DOWN is 4. If you are player #2, how might you induce player #1

to play DOWN so that you can get to a payoff of 4 instead of 2?Threaten to play down if player #1 plays UP.

Is such a threat credible? No, since if player #1 plays UP, you maximize your

payoff by playing up.

Solving dynamic games

Let us define a subgame to be a smaller game “embedded” in the complete game. In other words, starting from some point in the original game, a subgame includes all subsequent choices that must be made if players actually reach that point in the game.

This will allow us to test whether conjectural sub-strategies within a game are sequentially rational.

In our original game, there are three subgames: the original complete game and the games that begin at player #2’s decision nodes:

2 2u

d

u

d

5, 2

1, 0

4, 4

6, 0

Subgame Perfect Nash Equilibrium

A strategy profile is Subgame Perfect Nash Equilibrium [SPNE] if the strategies are a Nash equilibrium in every subgame.

How do we determine the subgame perfect Nash equilibrium to a dynamic game?

The approach is simple: We look ahead and reason backward. In other words, we use backward induction.

Backward induction involves identifying the smallest possible subgames and determining what the optimal choices are for the player involved. Then we replace these subgames with the implied payoffs, and solve the next highest level of subgames. This process is continued until the Nash moves for every possible subgame have been found.

1

2

2

3

3

2, 1, 2

1, 3, 4

3, 0, 1

4, 3, 3

1, 2, 6

2, 6, 0

U

D

u

d

u

d

D’

U’

U’

D’

Another example

1

2

2

3

3

2, 1, 2

1, 3, 4

3, 0, 1

4, 3, 3

1, 2, 6

2, 6, 0

U

D

u

d

u

d

U’

D’

U’

D’

Another example

Solution: Player #1 picks D. Player #2 picks u. Player #3 picks D’. And [D, u, D’] is subgame perfect Nash equilibrium.

81

Assume that Firm 1 will introduce its new cereal first (a sequential game).

Question– What will be the outcome of this game?

Modified Product Choice Problem

The Extensive Form of a Game

82

Sequential Games

The Extensive Form of a Game– Using a decision tree

• Work backward from the best outcome for Firm 1

The Extensive Form of a Game

83

Product Choice Game in Extensive Form

Crispy

Sweet

Crispy

Sweet

-5, -5

10, 20

20, 10

-5, -5

Firm 1

Crispy

Sweet

Firm 2

Firm 2

84

Sequential Games

The Advantage of Moving First– In this product-choice game, there is a clear

advantage to moving first.

85

Sequential Games

Assume: Duopoly

Firm/100 10 and 100

Production Total 30

21

21

===+=

+==−=

πPQQMC

QQQQP

The Advantage of Moving First

86

Sequential Games

Duopoly

25.56 50.112 50.7 and 5.7 15

First Moves 1 FirmFirm/50.112 15 and 5.7

CollusionWith

21

21

21

=====

====

ππ

π

PQQ

PQQ

The Advantage of Moving First

87

Choosing Output

Firm 1

7.5

Firm 2

112.50, 112.50 56.25, 112.50

0, 0112.50, 56.25

125, 93.75 50, 75

93.75, 125

75, 50

100, 100

10 15

7.5

10

15

88

Choosing Output

Firm 1

7.5

Firm 2

112.50, 112.50 56.25, 112.50

0, 0112.50, 56.25

125, 93.75 50, 75

93.75, 125

75, 50

100, 100

10 15

7.5

10

15

This payoff matrix illustrates various outcomes– Move together,

both produce 10– Question

• What if Firm 1 moves first?

89

How To Make the First Move– Demonstrate Commitment– Firm 1 must constrain his behavior to the

extent Firm 2 is convinced that he is committed

Threats, Commitments, and Credibility

90

Threats, Commitments, and Credibility

Strategic Moves– What actions can a firm take to gain

advantage in the marketplace?• Deter entry• Induce competitors to reduce output, leave, raise

price• Implicit agreements that benefit one firm

91

Empty Threats– If a firm will be worse off if it charges a low

price, the threat of a low price is not credible in the eyes of the competitors.

Threats, Commitments, and Credibility

92

Wal-Mart Stores’Preemptive Investment Strategy

Question– How did Wal-Mart become the largest retailer

in the U.S. when many established retail chains were closing their doors?

• Hint– How did Wal-Mart gain monopoly power?– Preemptive game with Nash equilibrium– https://www.youtube.com/watch?v=JzhkVjYbPks

93

The Discount Store Preemption Game

Wal-Mart

Enter Don’t enter

Enter

Don’t enter

Company X

-10, -10 20, 0

0, 00, 20

94

The Discount Store Preemption Game

Wal-Mart

Enter Don’t enter

Enter

Don’t enter

Company X

-10, -10 20, 0

0, 00, 20

Two Nash equilibrium

– Low left

– Upper right

Must be preemptive to win

Strategic Entry Barriers

Are there actions that an incumbent firm might take to deter entry by outsiders? In certain cases there may be. If the incumbent can make some binding commitment and communicate that to potential entrants prior to their decision to enter, then the incumbent may be able to forestall entry.

Consider the following example from AvinashDixit, “New Developments in Oligopoly Theory,” American Economic Review, May 1982, pp. 12-17.

Consider a two-stage game between an incumbent monopolist and a prospective entrant. The first stage is the latter's entry decision. If he stays out, the incumbent earns monopoly profits PM If entry occurs, the incumbent decides whether to fight a price war, with profits PW to each, or to share the market, with profits PD to each duopolist.

At each termination point the corresponding payoffs are shown, the first component being the incumbent's. It is assumed that PM > PD > 0 > PW , that is, duopoly is profitable but not as much as monopoly, while a price war is mutually destructive

In the above example, the strategy "War if entry" cannot be part of a perfect equilibrium. The entrant knows that the incumbent's optimal response to entry is sharing. Since PD > 0, he stands to gain by entering. Therefore this is the outcome in the perfect equilibrium.

Now suppose the incumbent has available a prior irrevocable commitment, such as incurring cost C in readiness to fight a price war. This does not affect his payoff if a war in fact occurs, but lowers it by C otherwise. The new three-stage game tree is shown below.

An incumbent who has made this commitment will find it optimal to fight in the event of entry if PW > PD - C. An entrant, knowing this, will stay out if the incumbent is committed, and enter if he is passive. The incumbent, knowing this in turn, will make the commitment if the ultimate payoff from doing so, PM - C, exceeds that from being passive, PD. Provided there exists a commitment whose cost satisfies PM – PD > C > PD -PW, it allows the incumbent to employ a credible threat and deter entry to his own advantage. Incidentally, the example also shows how a sequential equilibrium has to be solved backwards. The availability of such a commitment is a matter for each specific case. Sunk capacity is the most cited example.

There are two essential requirements: the commitment should be made (and made known) prior to the entrant's decision, and it should be irre-versible. The incumbent often has a natural advantage of the first move, although an unaware passive incumbent may find himself facing an aggressive committed entrant, when the roles are reversed and the incumbent must contemplate exit. Irreversibility is a matter of technology and institutions. For example, capacity serves the purpose only if it cannot be costlessly liquidated. Capital goods that depreciate rapidly, or ones for which an efficient resale market exists, are not useful instruments for an entry-deterring commitment.

How might this work in practice?

“Techdom’s Two Cold Wars,” WSJ, 7/22/09. http://gattonweb.uky.edu/faculty/troske/teaching/eco411/articles/Techdoms Cold War WSJ 22-07-09.pdf

“Haven’t Shareholders Had Enough Chicken?” WSJ, 4/4/01.

http://gattonweb.uky.edu/faculty/troske/teaching/eco411/articles/Shareholder Chicken WSJ 04-04-01.pdf

101

How might this work in practice?

Don’t underestimate you rivals willingness to fight: http://gattonweb.uky.edu/faculty/troske/teaching/eco411/articles/Jet Maker Bombardier Finds Bigger Proves Far From Better - WSJ.pdfAnd the fight continues:

https://www.wsj.com/articles/trudeau-and-may-join-forces-against-boeing-in-its-dispute-with-bombardier-1505761250.

102

First Mover Disadvantage

There may be a disadvantage to being the first mover– Have to make the initial investment in

developing a new product. Following firms can copy what you do and avoid the investment costs

– Trying to set a standard

103

Flexibility and Options

The value of commitments lies in creating inflexibilityHowever, when there is uncertainty,

flexibility is valuable since future options are kept openCommitments can sacrifice the value of the

options

104

Commitment-Flexibility Tradeoff

By waiting, a firm preserves its option value

By waiting, the firm also may allow its competitors to make preemptive investments

105

Preserving Flexibility

Modify the commitment as conditions evolveDelay commitment until better information is

available on profitability Make unprofitable commitments today to

preserve valuable options in the future

106

Flexibility and Real Options

A real option exists if future information can be used to tailor decisionsBetter information about demand can be

utilized by delaying implementation of projectsValue of real options may be limited by the

risk of preemptionKey managerial skill in spotting valuable

real options107

Implications

When operating in a sequential environment managers should1. Carefully define the sequence of moves2. Work backwards from the end to predict the

likely outcome of the interactions, making sure you assume your rival is acting optimally

3. Decide whether there is any credible commitment you can make to change your rivals prediction of your action

108

What Game Theory Can Teach Managers

Understand your business setting– Identify your rivals an how you interact

Place yourself behind you rivals desk– Consider the entire sequence of decisions– Start at the end and work backwards to

determine your best strategy, as well as your rivals best strategy

With a first mover advantage try and move first

109

What Game Theory Can Teach ManagersWith a first mover advantage try and move

first– If you can’t move first, decide if there are

credible steps you can take to induce your rivals to change their decisions and improve your outcome

With a second mover advantage, avoid moving first– Be unpredictable and maximize flexibility

Repetition facilitates cooperation110

111

Summary

A game is cooperative if the players can communicate and arrange binding contracts; otherwise it is noncooperative.

A Nash equilibrium is a set of strategies such that all players are doing their best, given the strategies of the other players.

112

Summary

Strategies that are not optimal for a one-shot game may be optimal for a repeated game.

Strategies such as tit-for-tat pricing can facilitate coordination but are difficult to implement.

Market structure affects the sustainability of cooperative pricing.

113

Summary

An empty threat is a threat that one would have no incentive to carry out.

To deter entry, an incumbent firm must convince any potential competitor that entry will be unprofitable.