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ECO 610-401

Monday, November 3 rd

Game Theory and Strategy: Repeated Games, Credibility, andCollusionReadings: Brickley et. al, Chapter 9:264-273;Hoyt, Lecture 6:13-19

Monday, November 10 th

Incentives and the Firm: An IntroductionIncentives and the Firm: Incentive CompensationReadings: Brickley et. al, Chapter 2:31-35; 10:280-285; 15



Market Structure & IndustryCompetition

PotentialEntrants

Threat of Entr

IndustryCompetitors

Rivalry amongExisting Firms

Suppliers

BargainingPower of

u lier Buy ers

BargainingPower of

Sub stit u tes

Threat of Substitute



Intensity of Rivalry among existingCompetitors

Intensity is greater when: Numerous or equally balanced competitors Slow industry growth High fixed or storage costs

Lack of differentiation or switching costs Capacity augmented in large increments Diverse goals of competitors High Stakes High Exit Barriers

Specialized AssetsFixed Costs of Exit Strategic Interrelationships



L eadership

Are there advantages to being a leader?When and how can a firm maintain a leadership position?In this section we examine two forms of leadership and show how it is advantageous to

be a leader.In the next section we discuss how a leadership position can be maintained.In particular, to be a leader the firm must:

y Be able to credibly commit to a strategyy K now competitors' responsesy Punish competitors if they don't follow.



Quantity Leadership

Is there an advantage in committing to production and sales goals first?Sta ckelburg model : Same as Cournot except 1 firm sets Q before the other firm.Result: The firm that moves 1st will have higher and output. This is because the

other firm knows that your Q cannot change and will cut his to keep price up.



Cournot vs. StackelburgStackelburg

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Q1

Q 2

1's Reaction

Function

2's ReactionFunction

Cournot

Stackelburg

Profits



Price Leadership and the Dominant Firm

Suppose instead a firm can set price (a dominant firm) and lets other firms sell asmuch as they want.

H ow does the dominant firm decide what price to set?Based on his residual demand - the demand for his product given how much the

smaller firms can supply



Pricing with a Dominant Firm

Supp ly f orSmall F irms

MC D DM

D D

M R D

P*

Q*



The Eightfold Path to Credibility

1. Establish and use a reputation.2. Write contracts3. Cut off communication.4. Burn bridges behind you.5. L eave the outcome to chance.6. M ove in small steps.

7. D evelop Credibility through Teamwork.8. Employ M andated Negotiating Agents



Commitment

3 major types of commitment:y U nequivocal movey Retaliation with continued retaliation depending on competitor's

moves.y No action

The 1st commitment can deter retaliation;the 2nd can deter threatening moves;the 3rd creates trust.



Market Signals

P rior Announcemen ts of move s

Reasons for prior annoucements: preempting the competition (Stackelburg 1st mover,must be credible)

threat (retaliation in a repeated game, again must be credible)

tests of competitor sentiment (how will competition respond?)communicating pleasure or displeasure with competitorsminimizing provocation



Communicating Commitment:

Commitment is more credible if:y firm has assets to retaliate or move (excess cash reserves, excess

productive capacity)y history of past adherence to commitments

y long term contractsy ability to detect compliance



C ompetitive Moves

Porter identifies 3 types of moves:C ooper at ive Or Non th re at ening T h re at ening

y K ey questions:y how likely is retaliation?

y how soon will retaliation come?y how effective will retaliation be?y how tough will retaliation be?y can retaliation be influenced?

D efen sive Move s

y M ost effective defense is to prevent a battle altogether. Thismeans that firm must commit to a credible retaliation.



Entry Deterence & Monopolization

How can firms maintain monopoly power?Key is to create barriers to entry:

How can this be done what strategies have been

used? What about the legality of proceedings?



Legal CasesWe can learn about some of the strategies (mostly illegal) by

examining cases: U.S. v. Aluminum Company of American (1945)

Strategy: Excess Capacity Telex v. IB M (1975)

Strategies: Predatory pricing, Product design FTC v. Xerox (1975)

Leasing & bundlingPatent Acquisition

FTC v. Kellogg (1981)

Brand Proliferation



U.S. v. Alcoa (1945)Issue 1: What is the market?

If include secondary ingots (scrap aluminum) 33% Primary ingots, 90% (no other American producers

This is what Judge Learned Hand choseIssue 2: Did it act to create monopoly or monopoly thrust upon it?

The argument for having monopoly thrust upon it:Market domination originated from patentsContinued because of:

Economies of scale in conversion of bauxite to aluminumoxide

Vertical integration Moderate pricing policy



U.S. v. Alcoa, continued

I ssue 3: Does it matter how the monopoly arises or how itbehaves?

From Judge Hand s decision: It was an excuse, that Alcoa had not abused its power, it

lay upon Alcoa to prove it had not. But the whole issue isirrelevant anyway

The Act (Sherman Antitrust, 1914) had widerpurposes Many people believe that possession of unchallenged economic power deadens initiative,discourages thrigt and depresses energy; that immunityfrom competition is a narcotic and rivalry is a stimulant to

industrial progess Congress did not condone good trusts and condemn badtrusts ; it forbade all.



U.S. v. Alcoa, 3Issue 4: But did Alcoa actively attempt to monopolize and how?From Hand s opinion:

not a pound of ingot has been produced by anyone elsein the United States [T]his continued control did not fallundesigned into Alcoa s lap; obviously it could not have

done so. It was not inevitable that is should always anticipateincreases in the demand for ingot and be prepared to supplythem. Nothing compelled it to keep doubling and redoublingits capacity before others entered the field.

Strategy: Excess Capacity as a deterent



Telex v. IB M (1975)

Facts: IBM dominated the rental market for mainframe C PU s for period

1964-1972 Also sold complete systems: C PU and periphals (terminals,

tapes, card readers) along with Burroughs and Honeywell Smaller firms (Telex) produced only peripheral equipment These smaller firms made significant inroads into IB M peripheralequipment (plug compatible) & charged much lower prices



Telex v. IB M (1975), 2

Facts:IBM s responses:

Cut price of peripheral equipment competing with Telex Redesigned equipment to make (artificially) more difficulty to

use Telex Lease agreements with reduced prices Large price reductions in peripheral equipment & large price

increases in C PU s



Telex v. IB M (1975), 3

The District Courts decision: Ruled in favor of IB M: As to pricing, the trial court found it was used by IB M only to a

limited extent, that is, within the reasonable range. The

resulting prices were reasonable in that they yielded reasonableprofits. The record shows, during the period under consideration, that

the parties and others in the market produced more advancedproducts better suited to the needs of the customers at lowerprices



Telex v. IB M (1975), 4

Strategies by IB M: Predatory pricing? Unnecessary product design to reduce compatibility



FTC v. Xerox

Facts: In 1973 Xerox had 86% of copier industry & 95% of

plain paper. Xerox used a lease only policy:

Package leasing plans & quantity discounts FTC claimed unfairly discriminated against customers

All service done by XeroxXerox had 1,700 patents & numerous cross-licensingagreements



FTC v. Xerox, 2

FTC claimed: Lease only policy unfairly discriminated against

customers

Reduced competition in supplies and services Patent policy allowed access to other firms patents Cross-licensing restricted competition



FTC v. Xerox, 4

Strategies by Xerox Leasing & bundling to control all aspects of copier

market (machines, repair, supplies)

Control of market by patent acquisition & cross-licensing



FTC v. Kellogg (1981)

Facts: Kellogg, General Mills, & General Foods had 80% of market but

no one firm controlled more than 45% FTC charged:

Firms had tacitly colluded & cooperated to maintain & exercisemonopoly powerThey did this by:

Avoid price competition Focus on raising barriers to entry:

» Excessive advertising

» Brand proliferation» Control of shelf space



FTC v. Kellogg (1981), 2

FTC Evidence: Extremely high profits in RTE cereal Lack of entry for decades

Case was dismissed: Our concept of a free competitive system does not envision

imposition by government of permissible levels of advertising

Brand proliferation is nothing more than the introduction of new brands which is a legitimate means of competition

Respondents engage in intense, unrestrained anduncoordinated competition in the introduction of newproducts.



Seq uential Move G ames

Now we consider sequential move games where both players respond to each other'smoves sequentially.

We represent the sequential aspects of the game using a decision tree.Consider the following examples:



Centipede Game

1

2

(1,0)

(0,4)

(2,2)

Take the

Money

Take theMoney

plit

Wait



IBM versus Telex

1

2

(1,5)

(-2,2)

(2,3)

tay Out

mash

ccommodate

nter



H ow do we find a solution?R ule 4: Look ahead and reason back.



A R epeated G ame in Prices (Sup ergame)

The Bertrand equilibrium (price competition) with its competitive result might seem a bit dissatisfying--two firms giving a competitive result.

Suppose the game could be played repeatedly--would our results change?For example, suppose two firms start with agreeing to the monopoly price and a firm

considers cheating this month by cutting its price a small amount.Will it want to do so if it believes that next period its competitor will cut his price to c

and ruin all profits?



F ini t e G a me

Each firm maximizes the present value of profits,

)( 211

1 p p

T

i

iT H §!

for firm 1

and

)( 21

2

1 p p

T

i

i

T H §! for firm 2

y dis the discount rate and is equal to e -rt where r is the instantaneous rate of interest and t is thtime between periods. Essentially future profits, because of alternative uses of funds woul

be discounted.y Profits for each firm depend on both firms' prices and the firms are assumed to be in busines

T years.

y Will the firms want to collude for at least some of the time?y What will the attern of rices be over time?



I nfini t e Horizon G a me s

The outcomes change when we consider games with infinite horizons.Suppose that both firms have the following strategy: charge the monopoly price, p m, in

period 0 and charge p m in period t if in every period preceding t its competitor charged p m; otherwise it sets its price at marginal cost, c, forever.

This strategy is referred to as a trigger strategy because a single deviation triggers a haltin cooperation.

Is a collusive agreement possible?



Firm 2P

M(11) P

M-I (3)

PM

(11) 50,50 0, 54Firm 1P

M-I (3) 54,0 27,27

Finite Game

Strategy:Start with P M

D o P M if competitor did P M

D o P=3 if competitor does P=3Will this yield P M for entire game?Answer: No -- last period both will cheat.



2 Possible Strategies

Punitive (Trigger)

Set high price in period 1

K eep price high in succeeding period if opponent hashigh price as well

If opponent has low price, set low prices for forever after

Tit for tat

Set high price in period 1Price in each succeeding period imitates previous price

of opponent



Mixed Strategies

Consider the game of Matching Pennies :

What is the equilibrium strategies?There is none in pure strategies

Adopt a random strategy. 1 plays Heads (H) p% of time & 2 plays Hq% of time.

But what strategy?

2H eads Tails

H eads +3, -1 -1,+31Tails -4, +1 +5,-2



Player 1 should choose the probability of playing H (p) to maximizepayoff given 2 s strategy (q):

T 1 = p(3q + (1-q)(-1)) + (1-p)(-4q + (1-q)4) = -5p + 12pq - 8q +3

Then xT 1 / xp = -5 + 12q = 0 q = 5/12

1 s choice gives 2 s strategy At q = 5/12 the expected payoff from 1 doing H & T are identical.



For 2 we have:T 2 = q(-p + (1-p)) + (1-q)(3p + (1-p)(-2))

= -7pq + 3q +5p - 2.

xT 2 / xq = 3 - 7p = 0 p = 3/7.



Wage and Employment Determination

The Basic Wage/Employment DecisionNoncompetitive Markets ( Monopsony)Training, Human Capital, and Wages

Job Market SignalingCompensating Wage DifferentialsIncentives & Principal Agent Problems



Competitive Labor Market

Firm chooses inputs (labor & capital) to maximize profits:

MR (MPP L)-w = MRPL-w = 0

MR (MPP K )-r = MRPK -r = 0



Profit- Maximizing Choice of Labor

w

L* L

M P L

Figure 1



Monoposonist

Single-buyer of labor Applications:

Specialized labor

Company town Implications:Upward-sloping supply curveWage < Marginal Factor Cost ( MFC)Why? Need to raise wage to induce more to work but need to do it for all workers



Table 1

L MRP w MFC wL

0

1 20 5.27 5.27 5.27

2 15.16 6.01 6.76 12.03

3 12.89 6.64 7.89 19.92

4 11.49 7.2 8.87 28.79

5 10.51 7.71 9.76 38.54

6 9.77 8.19 10.59 49.13

7 9.18 8.64 11.36 60.49

8 8.71 9.07 12.1 72.59

9 8.3 9.49 12.8 85.39

10 7.96 9.89 13.48 98.88

11 7.66 10.27 14.14 113.01

12 7.4 10.65 14.77 127.78

13 7.17 11.01 15.39 143.17

14 6.96 11.37 15.99 159.15

15 6.77 11.71 16.57 175.72

16 6.6 12.05 17.14 192.86

17 6.44 12.39 17.7 210.57



Fig re 2

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

L

M R P , w

M FC

W

w M

LM LC



Training, Human Capital, & Lifetime Wages

Many firms pay for training and education for employeesHow does this affect salaries both after & duringtraining?

We distinguish between two types: Specific General



Training (continued)

Some Notation:W0 - wage in period 0;W1 - wage in period 1;

MP0 - marginal productivity in period 0;MP1 - marginal productivity in period 1;Z - training costs;r - discount rate;

W* - wage in alternative employment (both periods).



Specific Training

A Numerical Example:W*, the alternative wage, = $50,000Discount rate is 10%.P V of alternative wage is 95,450Net marginal productivity in the first period MP0 - Z = $40,000Net marginal productivity in the second period is $61,000.How will the worker be paid?2 conditionsP V of the earnings in the two period must equal $95,450.Earnings in period 2, W 1 > W* = $50,000 < MP1 = $61,000.If W0 = $45,000 and W 1=$55,500 all these conditions are satisfied.



Specific Training, GraphicalFigu re 3

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

62

0 1 2

Q

M P

,

¡

$ 1

, 0 0 0¢

P er iod 0P er iod 1

*

MP 0-Z

MP 1

0

W 1



General Training

How does compensation change if it is general ratherthan specific training?Worker has higher productivity in the firm paying for thetraining and elsewhere.Then: Either binding commitment for remaining in firm

following training Or, pay W

1= MP

1 what other firms will pay

If so, then W o = MPo Z in fact, worker pays fortraining.



Compensating Wage Differentials

Differences in wages among workers can be explainedby a number of factors including: Education & Training

Skills Experience Discrimination Characteristics of employment

UnpleasantnessInjuryRiskLocation



Compensating Wage Differentials (2)

Differences in wages due to differences in job conditionsare referred to as compensating wage differentialsFor individuals to be willing to take jobs with greaterrisks, everything else equal, they require greatercompensation



Example: AIDS & Nursing



Findings

Men facing average fatal risk are paid compensation(relative to no risk) $166 to $277 a year (.53 to .89%)

Men facing average non-fatal risk are paid compensation(relative to no risk) $240 to $429 a year (.93 to 1.38%)Women facing average non-fatal risk are paidcompensation (relative to no risk) $714 to $1,119 a year (2.87 to 4.49%)



Regulation & Workplace Hazards

Value of LifeWhat is meant by it & how might it be measured? One notion: Forgone earnings in the event of death

Another notion: How much would you need to becompensated for a (small) increase in the probabilityof death?

Value of Life=(Compensation)/(Change in Risk)

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