Strategic Interaction

Finance 510: Microeconomic Analysis

Market Structures

Recall that there is an entire spectrum of market structures

Perfect Competition

Many firms, each with zero market share

P = MC

Profits = 0 (Firm’s earn a reasonable rate of return on invested capital

NO STRATEGIC INTERACTION!

Monopoly

One firm, with 100% market share

P > MC

Profits > 0 (Firm’s earn excessive rates of return on invested capital)

NO STRATEGIC INTERACTION!

Most industries, however, don’t fit the assumptions of either perfect competition or monopoly. We call these industries oligopolies

Oligopoly

Relatively few firms, each with positive market share

STRATEGIC INTERACTION!

Wireless (2002)

Verizon: 30% Cingular: 22% AT&T: 20% Sprint PCS: 14% Nextel: 10% Voicestream: 6%

US Beer (2001)

Anheuser-Busch: 49% Miller: 20% Coors: 11% Pabst: 4% Heineken: 3%

Music Recording (2001)

Universal/Polygram: 23% Sony: 15% EMI: 13% Warner: 12% BMG: 8%

Further, these market shares are not constant over time!

9

11

14

15

20

21

Airlines (1992) Airlines (2002)

American

Northwest

Delta

United

Continental

US Air 7

9

11

15

17

19American

United

Delta

Northwest

Continental

SWest

While the absolute ordering didn’t change, all the airlines lost market share to Southwest.

Another trend is consolidation

44

55

677

888

9

Retail Gasoline (1992) Retail Gasoline (2001)

Shell

ExxonTexaco

Chevron

Amoco

Mobil

7

10

16

18

20

24Exxon/Mobil

Shell

BP/Amoco/Arco

Chev/Texaco

Conoco/PhillipsCitgoBP

Marathon

SunPhillips

Total/Fina/Elf

The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions

Monopoly

PQQ Oligopoly

NPPPQQ ,..., 1

Your Price (-)

Your N Competitors Prices (+)

Oligopolistic markets rely crucially on the interactions between firms which is why we need game theory to analyze them!

The Airline Price Warsp

Q

$500

$220

60 180

Suppose that American and Delta face the given aggregate demand for flights to NYC and that the unit cost for the trip is $200. If they charge the same fare, they split the market

P = $500 P = $220

P = $500 $9,000

$9,000

$3,600

$0

P = $220 $0

$3,600

$1,800

$1,800

American

Del

taWhat will the equilibrium be?

Assume that Delta has the following beliefs about American’s Strategy

220$Pr

500$Pr

P

P

r

l

Probabilities of

choosing High or Low price

Player A’s best response will be his own set of probabilities to maximize expected utility

220$Pr

500$Pr

Pp

Pp

b

t

)1800($)3600($)0()9000($,

rlbrltpp

ppMaxbt

The Airline Price Wars

btbt

rlbltbt

pppp

pppp

211

)1800($)3600($000,9$),,(

Subject to

0

0

1

b

t

bt

p

p

pp Probabilities always have to sum to one

Both Prices have a chance of being chosen

)1800($)3600($)0()9000($,

rlbrltpp

ppMaxbt

First Order Necessary Conditions

09000 1 l 018003600 2 rl

01 bt pp

01 tp02 bp

02 01

0tp0bp

0

0

b

t

p

p

021

1

180036009000

lr

rll

4

3

4

1 rl

btbt

rlbltbt

pppp

pppp

211

)1800($)3600($000,9$),,(

4

3

4

1 rl pp

4

3

4

1 bt pp

0 1 rl pp 0 1 bt pp

1 0 rl pp 1 0 bt pp

Both always charge $500

Both always charge $220

Both Randomize between $500 and $220

Notice that prices are low most of the time!

The Airline Price Wars

Continuous Choice Games – Cournot Competitionp

QD

There are two firms in an industry – both facing an aggregate (inverse) demand curve given by

BQAP

Aggregate Production

Both firms have constant marginal costs equal to $C

From firm one’s perspective, the demand curve is given by

1221 BqBqAqqBAP

Treated as a constant by Firm One

212 1BqqBqATR

Solving Firm One’s Profit Maximization…

cBqBqAMR 12 2

B

cBqAq

22

1

21 2

1

2q

B

cAq

In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2

1q

2q

B

cA

B

cA

2

Note that this is the optimal output for a monopolist!

Further, if Firm two produces

1q

2q

B

cA

B

cA

2

B

cA It drives price down to MC

BQAP

cB

cABAP

21 2

1

2q

B

cAq

The game is symmetric with respect to Firm two…

1q

2q

12 2

1

2q

B

cAq

B

cA

Firm 1

Firm 2

B

cA

2

B

cA

2

B

cA

1q

2q

Firm 1

Firm 2

*

1q

*2q

B

cAqq

3

1*2

*

1

B

cAqqQ

3

2*2

*

1

B

cA

B

cA

B

cA

3

2

2

1

Monopoly Output

Competitive Output

There exists a unique Nash equilibrium

A numerical example…

Suppose that the market demand for computer chips (Q is in millions) is given by

QP 20120

Intel and Cyrix are both competing in the market and have a marginal cost of $20.

Mqq CI 67.13

5

20

20120

3

1**

33.53$)33.3(20120 P

Had this market been serviced instead by a monopoly,

70$)5.2(20120

5.2*

P

MQ

20$

20120

MC

QP

1

1

MCp

4.15.2

70

20

1

Q

P

dP

dQ

4.11

1

20$70$

With competing duopolies

33.53$)67.1(206.86

67.1*

P

MQ

1

1

MCp

6.167.1

33.53

20

1

iQ

P

dP

dQ

6.11

1

20$33.53$

20$

206.862020120 112

MC

qqqP

One more point…

125$5.2)20$70($

70$

5.2*

P

MQ

55$67.1)2053($

33.53$

67.1*

P

MQ

Monopoly Duopoly

If both firms agreed to produce 1.25M chips (half the monopoly output), they could split the monopoly profits ($62.5 apiece). Why don’t these firms collude?

Suppose we increase the number of firms…

N

iiqBABQAP

1

Demand facing firm i is given by (MC = c)

iij j BqqBAP

iQ

iQB

cAq

2

1

21

ii QB

cAq

2

1

2

Firm i’s best response to its N-1 competitors is given by

ii qNQ )1( Further, we know that all firms produce the same level of output.

Solving for price and quantity, we get

BN

cAqi )1(

BN

cANQ

)1(

cN

N

N

AP

11

Expanding the number of firms in an oligopoly

BN

cAqi )1(

BN

cANQ

)1(

cN

N

N

AP

11

Note that as the number of firms increases:

Output approaches the perfectly competitive level of production

Price approaches marginal cost.

Lets go back to the previous example…

20$

20120

MC

QP

p

QD

$53

3.33

CS = (.5)(120 – 53)(3.33) = $112

$112

What would it be worth to consumers to add another firm to the industry?

56$

33.53$

33.32

67.1*

P

qQ

Mq

Recall, we had an aggregate demand for computer chips and a constant marginal cost of production.

20$

20120

MC

QP

p

QD

$45

3.75

CS = (.5)(120 – 45)(3.75) = $140

$140

31$

45$

75.33

25.1*

P

qQ

Mq

With three firms in the market…

A 25% increase in CS!!

0

1

2

3

4

5

6

Number of Firms

0

10

20

30

40

50

60

70

80

Firm Sales Industry Sales Price

Increasing Competition

Increasing Competition

0

50

100

150

200

250

300

Number of Firms

Consumer Surplus Firm Profit Industry Profit

20$

20120

MC

QP

Now, suppose that there were annual fixed costs equal to $10

How many firms can this industry support?

BN

cAqi )1(

c

N

N

N

AP

11

010$)20$( ii qP Solve for N

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

With a fixed cost of $10, this industry can support 7 Firms

21 2

1

2q

B

cAq

1q

2q

12 2

1

2q

B

cAq

Firm 1

Firm 2

The previous analysis was with identical firms.

*2q

*1q

Suppose Firm 2’s marginal costs are greater than Firm 1’s….

21

1 2

1

2q

B

cAq

1q

2q

12

12

2 2

1

2

cc

qB

cAq

Firm 1

Firm 2*2q

*1q

Suppose Firm 2’s marginal costs are greater than Firm 1’s….

Firm 2’s market share drops

B

ccAq

3

2 12*

1

B

ccAq

3

2 21*

2

B

ccAQ

3

2 21

+

As long as average industry costs are the same as the identical firm case

ccc

2

21

Industry output and price are unaffected!

Note, however, that production is undertaken in an inefficient manner!

With constant marginal costs, the firm with the lower cost should be supplying the entire market!!

Market Concentration and Profitibility

N

iiqBAP

1

Industry Demand

ii s

P

cP

000,10

H

P

cP

The Lerner index for Firm i is related to Firm i’s market share and the elasticity of industry demand

The Average Lerner index for the industry is related to the HHI and the elasticity of industry demand

The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable.

p

QD

Q*

P*

Should it matter?

BQAP Just as before, we have an industry demand curve and two competing duopolists – both with marginal cost equal to c.

1qD

BQAP

Bb

B

Aa

bPaQ

1

Cournot Case

1p

1qD

Bertrand Case

2BqA

1p

2p

Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits

2111

211

1

21

211

))((

2

)(

0

,

ppifbpacp

ppifbpa

cp

ppif

pp

As in the cournot case, we need to find firm one’s best response (i.e. profit maximizing response) to every possible price set by firm 2.

Firm One’s Best Response Function

mpp 2

Case #1: Firm 2 sets a price above the pure monopoly price:

2pc Case #3: Firm 2 sets a price below marginal cost

cppm 2

Case #2: Firm 2 sets a price between the monopoly price and marginal cost

mpp 1

21 pp

21 pp

2pc Case #4: Firm 2 sets a price equal to marginal cost

cpp 21

What’s the Nash equilibrium of this game?

Bertrand Equilibrium: It only takes two firm’s in the market to drive prices to marginal cost and profits to zero!

However, the Bertrand equilibrium makes some very restricting assumptions…

Firms are producing identical products (i.e. perfect substitutes)

Firms are not capacity constrained

An example…capacity constraints

Consider two theatres located side by side. Each theatre’s marginal cost is constant at $10. Both face an aggregate demand for movies equal to

PQ 60000,6 Each theatre has the capacity to handle 2,000 customers per day.

What will the equilibrium be in this case?

PQ 60000,6 If both firms set a price equal to $10 (Marginal cost), then market demand is 5,400 (well above total capacity = 2,000)

Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability to make a credible threat:

“If you set a price above marginal cost, I will undercut you and steal all your customers!”

33.33$

60000,6000,4

P

P

At a price of $33, market demand is 4,000 and both firms operate at capacity

Imperfect SubstitutesRecall our previous model that included travel time in the purchase price of a product

Firm 1Customer

x

txpp ~

Dollar Price

Distance to Store

Travel Costs

Length = 1

Consumers places a value V on the product

Imperfect Substitutes

Now, suppose that there are two competitors in the market – operating at the two sides of town

Firm 1Customer

x

Firm 2

x1

)1(~~21 xtpVtxpV

The “Marginal Consumer” is indifferent between the two competitors.

We can solve for the “location” of this customer to get a demand curve

Imperfect Substitutes

t

tppx

212

Firm 1Customer

x

Firm 2

x1

Nt

tppD

2

121 N

t

tppNxD

2

)1( 212

Both firms have a marginal cost equal to c

Nt

tppcp

2

)( 1211

Nt

tppcp

2

)( 2122

Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price.

2

21

ctpp

2

12

ctpp

1p

2p

Firm 1

Firm 2

2

ct

2

ct

ct

ct

Bertrand Equilibrium with imperfect substitutes

Cournot vs Bertrand

1p

2pFirm 1

Firm 2

1q

2q

Firm 1

Firm 2

Suppose that Firm two‘s costs increase. What happens in each case?

Bertrand Cournot

Cournot vs Bertrand

Suppose that Firm two‘s costs increase. What happens in each case?

Cournot (Quantity Competition): Competition is very aggressive

Firm One responds to firm B’s cost increases by expanding production and increasing market share\

Best response strategies are strategic substitutes

Bertrand (Price Competition): Competition is very passive

Firm One responds to firm B’s cost increases by increasing price and maintaining market share

Best response strategies are strategic complements

Stackelberg leadership – Quantity Competition

In the previous example, firms made price/quantity decisions simultaneously. Suppose we relax that and allow one firm to choose first.

BQAP

Both firms have a marginal cost equal to c

Firm A chooses its output first

Firm B chooses its output second

Market Price is determined

Firm B has observed Firm A’s output decision and faces the residual demand curve:

BA BqBqAP

2BBA BqqBqATR

cBqBqAMR BA 2

ABA

B qqq

B

cAq

22

Knowing Firm B’s response, Firm A can now maximize its profits:

AB BqBqAP

22A

B

q

B

cAq

22ABqcA

P

22

2

ABqqcA

TR A

cBq

cAMR A

2

B

cAqA 2

Monopoly Output

B

cAqA 2

22A

B

q

B

cAq

B

cAqB 4

B

cAqq BA 4

3

B

cA

B

cA

B

cA

B

cA

4

3

3

2

2

1

Monopoly Output

Competitive Output

Cournot Output

Stackelberg Output

Essentially, Firm B acts as a monopoly in the “Secondary” market (i.e. after A has chosen). Firm B earns lower profits!

2

21

ctpp

2

12

ctpp

Sequential Bertrand Competition

With identical products, we get the same result as before (P = MC). However, lets reconsider the imperfect substitute case.

We already derived each firm’s best response functions

Now, suppose that Firm 1 gets to set its price first (taking into account firm 2’s response)

Nt

tppcp

2

)( 1211

Sequential Bertrand Competition

Nt

ptccp

4

3)( 1

11

Take the derivative and set equal to zero to maximize profits

2

31

tcp

4

5

21

2

tc

ctpp

Note that prices are higher than under the simultaneous move example!!

ND8

31

Sequential Bertrand Competition

2

31

tcp

4

5

21

2

tc

ctpp

ND8

52

Nt32

181 Nt

32

252

In the simultaneous move game, Firm A and B charged the same price, split the market, and earned equal profits. Here, there is a second mover advantage!!

Cournot vs Bertrand: Stackelberg Games

Cournot (Quantity Competition):

Firm One has a first mover advantage – it gains market share and earns higher profits. Firm B loses market share and earns lower profits

Total industry output increases (price decreases)

Bertrand (Price Competition):

Firm Two has a second mover advantage – it charges a lower price (relative to firm one), gains market share and increases profits.

Overall, production drops, prices rise, and both firms increase profits.