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ECO 610-401 –Monday, November 3 rd Game Theory and Strategy: Repeated Games, Credibility, and Collusion Readings: Brickley et. al, Chapter 9:264-273; Hoyt,

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Presentation on theme: "ECO 610-401 –Monday, November 3 rd Game Theory and Strategy: Repeated Games, Credibility, and Collusion Readings: Brickley et. al, Chapter 9:264-273; Hoyt,"— Presentation transcript:

1 ECO 610-401 –Monday, November 3 rd Game Theory and Strategy: Repeated Games, Credibility, and Collusion Readings: Brickley et. al, Chapter 9:264-273; Hoyt, Lecture 6:13-19 –Monday, November 10 th Incentives and the Firm: An Introduction Incentives and the Firm: Incentive Compensation Readings: Brickley et. al, Chapter 2:31-35; 10:280-285; 15

2 Market Structure & Industry Competition

3 Intensity of Rivalry among existing Competitors 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 Assets Fixed Costs of Exit Strategic Interrelationships

4 Leadership 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:  Be able to credibly commit to a strategy  Know competitors' responses  Punish competitors if they don't follow.

5 Quantity Leadership Is there an advantage in committing to production and sales goals first? Stackelburg model: Same as Cournot except 1 firm sets Q before the other firm. Result: The firm that moves 1st will have higher π and output. This is because the other firm knows that your Q cannot change and will cut his to keep price up.

6 Cournot vs. Stackelburg

7 Price Leadership and the Dominant Firm Suppose instead a firm can set price (a dominant firm) and lets other firms sell as much as they want. How 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

8 Pricing with a Dominant Firm D MR D P*P* Q*Q*

9 The Eightfold Path to Credibility 1. Establish and use a reputation. 2. Write contracts 3. Cut off communication. 4. Burn bridges behind you. 5. Leave the outcome to chance. 6. Move in small steps. 7. Develop Credibility through Teamwork. 8. Employ Mandated Negotiating Agents

10 Commitment 3 major types of commitment:  Unequivocal move  Retaliation with continued retaliation depending on competitor's moves.  No action The 1st commitment can deter retaliation; the 2nd can deter threatening moves; the 3rd creates trust.

11 Market Signals Prior Announcements of moves 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 competitors minimizing provocation

12 Communicating Commitment: Commitment is more credible if:  firm has assets to retaliate or move (excess cash reserves, excess productive capacity)  history of past adherence to commitments  long term contracts  ability to detect compliance

13 Competitive Moves Porter identifies 3 types of moves: Cooperative Or Nonthreatening Threatening  Key questions:  how likely is retaliation?  how soon will retaliation come?  how effective will retaliation be?  how tough will retaliation be?  can retaliation be influenced? Defensive Moves  Most effective defense is to prevent a battle altogether. This means that firm must commit to a credible retaliation.

14 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?

15 Legal Cases We 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. IBM (1975) Strategies: Predatory pricing, Product design –FTC v. Xerox (1975) Leasing & bundling Patent Acquisition –FTC v. Kellogg (1981) Brand Proliferation

16 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 chose Issue 2: Did it act to create monopoly or monopoly thrust upon it? –The argument for having monopoly thrust upon it: Market domination originated from patents Continued because of: –Economies of scale in conversion of bauxite to aluminum oxide –Vertical integration –Moderate pricing policy

17 U.S. v. Alcoa, continued Issue 3: Does it matter how the monopoly arises or how it behaves? 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 is irrelevant anyway… –“The Act (Sherman Antitrust, 1914) had wider purposes…Many people believe that possession of unchallenged economic power deadens initiative, discourages thrigt and depresses energy; that immunity from competition is a narcotic and rivalry is a stimulant to industrial progess –“Congress did not condone “good trusts” and condemn “bad trusts”; it forbade all.”

18 U.S. v. Alcoa, 3 Issue 4: But did Alcoa actively attempt to monopolize and how? From Hand’s opinion: –“…not a pound of ingot has been produced by anyone else in the United States …[T]his continued control did not fall undesigned into Alcoa’s lap; obviously it could not have done so. –“It was not inevitable that is should always anticipate increases in the demand for ingot and be prepared to supply them. Nothing compelled it to keep doubling and redoubling its capacity before others entered the field. Strategy: Excess Capacity as a deterent

19 Telex v. IBM (1975) Facts: –IBM dominated the rental market for mainframe CPU’s for period 1964-1972 –Also sold complete systems: CPU 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 IBM peripheral equipment (plug compatible) & charged much lower prices

20 Telex v. IBM (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 CPU’s

21 Telex v. IBM (1975), 3 The District Courts decision: –Ruled in favor of IBM: –“As to pricing, the trial court found it was used by IBM only to a limited extent, that is, within the “reasonable” range. The resulting prices were reasonable in that they yielded reasonable profits.” –“The record shows, during the period under consideration, that the parties and others in the market produced more advanced products better suited to the needs of the customers at lower prices…”

22 Telex v. IBM (1975), 4 Strategies by IBM: –Predatory pricing? –Unnecessary product design to reduce compatibility

23 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 Xerox Xerox had 1,700 patents & numerous cross-licensing agreements

24 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

25 FTC v. Xerox, 3 Consent Decree signed by FTC & Xerox: –No royalty on several of patents it was to license –To refrain from acquiring patent licenses –To eliminate pricing plans based on quantity leasing or purchasing plans –To offer copiers for sale as well as lease

26 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

27 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 & exercise monopoly power” They did this by: –Avoid price competition –Focus on raising barriers to entry: »Excessive advertising »Brand proliferation »Control of shelf space

28 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 and uncoordinated competition in the introduction of new products.”

29 Sequential Move Games Now we consider sequential move games where both players respond to each other's moves sequentially. We represent the sequential aspects of the game using a decision tree. Consider the following examples:

30 Centipede Game

31 IBM versus Telex

32 How do we find a solution? Rule 4:Look ahead and reason back.

33 A Repeated Game in Prices (Supergame) 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?

34 Finite Game

35 Infinite Horizon Games 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 halt in cooperation. Is a collusive agreement possible?

36 Finite Game Game is 10 periods Demand is P = 21 - Q 1 -Q 2 MC = 1 Monopoly P=11, Profit=100

37 Finite Game Strategy: Start with P M Do P M if competitor did P M Do P=3 if competitor does P=3 Will this yield P M for entire game? Answer: No -- last period both will cheat.

38 2 Possible Strategies Punitive (Trigger) Set high price in period 1 Keep price high in succeeding period if opponent has high price as well If opponent has low price, set low prices for forever after Tit for tat Set high price in period 1 Price in each succeeding period imitates previous price of opponent

39 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 H q% of time. But what strategy?

40 Player 1 should choose the probability of playing H (p) to maximize payoff given 2’s strategy (q):  1 = p(3q + (1-q)(-1)) + (1-p)(-4q + (1-q)4) = -5p + 12pq - 8q + 3 Then  1 /  p = -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.

41 For 2 we have:  2 = q(-p + (1-p)) + (1-q)(3p + (1-p)(-2)) = -7pq + 3q +5p - 2.  2 /  q = 3 - 7p = 0  p = 3/7.

42 Wage and Employment Determination The Basic Wage/Employment Decision Noncompetitive Markets (Monopsony) Training, Human Capital, and Wages Job Market Signaling Compensating Wage Differentials Incentives & Principal Agent Problems

43 Competitive Labor Market Firm chooses inputs (labor & capital) to maximize profits: MR (MPP L )-w = MRP L -w = 0 MR (MPP K )-r = MRP K -r = 0

44 Profit-Maximizing Choice of Labor

45 Monoposonist Single-buyer of labor –Applications: Specialized labor “Company” town –Implications: Upward-sloping supply curve Wage < Marginal Factor Cost (MFC) Why? Need to raise wage to induce more to work – but need to do it for all workers

46 Table 1 L MRPwMFCwL 0 1205.27 312.896.647.8919.92 411.497.28.8728.79 510.517.719.7638.54 69.778.1910.5949.13 79.188.6411.3660.49 88.719.0712.172.59 98.39.4912.885.39 107.969.8913.4898.88 117.6610.2714.14113.01 127.410.6514.77127.78 137.1711.0115.39143.17 146.9611.3715.99159.15 156.7711.7116.57175.72 166.612.0517.14192.86 176.4412.3917.7210.57 186.2912.7118.25228.82 196.1613.0318.79247.6 206.0313.3519.32266.92


48 Training, Human Capital, & Lifetime Wages Many firms pay for training and education for employees How does this affect salaries both after & during training? We distinguish between two types: –Specific –General

49 Training (continued) Some Notation: W 0 - wage in period 0; W 1 - wage in period 1; MP 0 - marginal productivity in period 0; MP 1 - marginal productivity in period 1; Z - training costs; r - discount rate; W* - wage in alternative employment (both periods).

50 Specific Training A Numerical Example: W*, the alternative wage, = $50,000 Discount rate is 10%. PV of alternative wage is 95,450 Net marginal productivity in the first period MP0 - Z = $40,000 Net marginal productivity in the second period is $61,000. How will the worker be paid? 2 conditions PV of the earnings in the two period must equal $95,450. Earnings in period 2, W 1 > W* = $50,000 { "@context": "", "@type": "ImageObject", "contentUrl": "", "name": "Specific Training A Numerical Example: W*, the alternative wage, = $50,000 Discount rate is 10%.", "description": "PV of alternative wage is 95,450 Net marginal productivity in the first period MP0 - Z = $40,000 Net marginal productivity in the second period is $61,000. How will the worker be paid. 2 conditions PV of the earnings in the two period must equal $95,450. Earnings in period 2, W 1 > W* = $50,000

51 Specific Training, Graphical

52 General Training How does compensation change if it is general rather than specific training? Worker has higher productivity in the firm paying for the training 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 = MP o – Z – in fact, worker pays for training.

53 Compensating Wage Differentials Differences in wages among workers can be explained by a number of factors including: –Education & Training –Skills –Experience –Discrimination –Characteristics of employment Unpleasantness Injury Risk Location

54 Compensating Wage Differentials (2) Differences in wages due to differences in job conditions are referred to as compensating wage differentials For individuals to be willing to take jobs with greater risks, everything else equal, they require greater compensation

55 Example: AIDS & Nursing





60 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 paid compensation (relative to no risk) –$714 to $1,119 a year (2.87 to 4.49%)

61 Regulation & Workplace Hazards Value of Life What 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 be compensated for a (small) increase in the probability of death? –Value of Life=(Compensation)/(Change in Risk)




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