ECO 610-401

1. ECO 610-401 • Monday, October 27th • Market Structure: Price and Output with Market Power (continued) • Game Theory and Strategy: Simultaneous Moves • Readings: Brickley et. al, Chapter 9:251-263; • Hoyt, Lecture 6:1-13 • Monday, November 3rd • Game Theory and Strategy: Repeated Games, Credibility, and Collusion • Readings: Brickley et. al, Chapter 9:264-273; • Hoyt, Lecture 6:13-19

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. Market Structure and Equilibrium Price • Game 3: Duopoly (price competition) • 20 “buyers” with a reservation price • Each buyers 1 unit • Can’t pay more than that, want to pay less • 2 “Sellers” who can sell as much as they want at a (marginal) cost of $2 per unit • Seller 1 picks “price” • Buyers respond to price (note if they want to buy) • Seller 2 can pick a price • Buyers respond to price (note if they want to buy) • & continue until a seller is not willing to respond (change price) • Then sales are made at that price

5. Market Structure and Equilibrium Price • Game 4: Duopoly (quantity competition) • 20 “buyers” with a reservation price • Each buyer 1 unit • Can’t pay more than that, want to pay less • 2 “Sellers” who can sell as much as they want at $2 • Both sellers picks “quantities” • Then prices are called out until # buyers= quantity picked • Sellers can pick new quantities if they want • Then prices are called out until # buyers= quantity picked • & continue until a seller is not willing to respond (change quantity) • Then sales are made at price that clears

6. Oligopoly, Game Theory, and Competitive Strategy • Outline • Introduction • Elements of Game Theory and the Concept of Equilibrium • Applications of Simultaneous Move Games to Firm Strategy: Quantity v. Price Competition • Mixed Strategies • Sequential Move Games • Leadership • Applications of Game Theory and Competitive Strategy

7. A. Introduction Firms in perfect competition, monopoly, and monopolistic competition do not worry about the reactions of other firms in the industry. • For the competitive and monopolistically competitive firms, this is because any firm has a small share of the market. • For the monopoly there are no firms which produce a similar product. • For many industries this independence among firms does not exist. • Decisions by one firm will affect other firms producing like or similar products. • These industries, characterized by a few firms, are generally referred to as oligopolies.

8. Interdependence among Firms • Because this interdependence between firms we can expect to observe that oligopolistic firms will: • Base any actions they make including • pricing • output • research • advertising and marketing • on what they believe the response of other firms will be. • They have an incentive to cooperate or collude.

9. Example: The Demand for GM Automobiles • Demand for a product (GM automobile) depends on price of substitutes (Ford, Chrysler) Success of price changes depends on response of other firms

10. PGM DPFord high DPFord low QGM

11. Mathematical game theory Mathematical game theory was developed to analyze situations when the benefits players (firms) receive depends on the actions of other players. We shall use some of the concepts of mathematical game theory to explore the strategies of firms in oligopolistic markets. • In particular, we shall find that mathematical game theory will lead to predictions about: • firms competing in prices v. quantity; • when collusive agreements are likely to exist; • why firms differentiating products; and • strategies to deter entry.

12. An Example of Oligopolistic Behavior: The Robinson-Chamberlain Model Suppose that in the industry (automobile) that firms do not want to lose market share. Then: • If a firm cut volume (to raise price) it will do it alone -- other firms will not follow. • If a firm increases volume (lowering price) other firms will follow to avoid losing market share. • Then if the firm increases volume it will not gain market share as all the other will follow. • It keeps same market share and picks up sales according to market share. • Price drops significantly since all firms increase volume, • If it cuts volume it will lose share and price does not increase since other firms will not respond by cutting back volume.

13. Let the initial price of the GM automobile be P* and the initial output be Q*. Given the assumptions discussed above • What does the demand curve look like if GM increases its price above the competitors (who do not increase their prices) -- how steep or flat is it? • What does the demand curve look like if GM decreases its price (and so do the competitors) -- how steep or flat is it? • What does the marginal revenue curve look like?

14. The “Kinked” Demand Curve D MC MR

15. Model implies: • Price Rigidity in Oligopolies • Consistent with notion that “market share” is a firm objective; • Not entirely consistent with profit maximization

16. Game Theory and Firm Strategy • Mathematical game theory, as applied to firm strategy, motivates the following conclusions about firm strategies and market outcomes: • 1) Show the interdependence of firms • 2) Elasticity of demand is also related to the number of competitors. • 3) Non-cooperative strategy can yield profits, but less than in monopoly.

17. 4) In a single period game that firms would want to compete in Q not P because of higher π.. • 5) Show that if firms do compete in price it is to their advantage to differentiate products. • 6) A collusive agreement with price competition is price leadership, in which a dominant firm sets price and others follow. • 7) If we consider competition over time, price > marginal cost with price competition if firms make it clear that they will punish cheaters on the agreement. • 8) Leadership is only effective if firm is committed to the policy and/or has the ability to retaliate.

18. B. Elements of Game Theory and the Concept of Equilibrium • 1. Structure of a Game • 1) Players • 2) Strategies available to players (actions that can be taken) • 3) Payoffs earned by players that depend on the choices of every player • For a game to exist this information is necessary even if only available in a probabilistic sense (i.e., you don't know for certain what the payoff is).

19. Dominant Strategy -- A strategy is said to be dominant if it always results in the highest payoff to a player regardless of the strategies of other players. • What strategy should Kroger's choose? • Does it depend on Meijer's strategy? • Does it have a dominant strategy? • What about Meijer? • Does its strategy depend on Kroger's strategy? • Does it have a dominant strategy?

20. Other Examples

21. Prisoner’s Dilemna

22. Rule 1: If you have a dominant strategy, use it.

23. Dominated Strategies • Dominated Strategy -- A strategy is said to be dominated if there exists some other strategy that always has a higher payoff (or equal payoff) regardless of the strategies of opponents. • Consider a slightly different setting for competition between Kroger's and Meijer: • In this game we consider adding another strategy, running specials on bakery items. • Payoffs for the other strategies have also changed. • How will the bakery option affect the decisions of Kroger's and Meijer?

25. Rule 2: Eliminate all dominated strategies.

26. It is clear what Kroger's should do -- run the deli since it is a dominant strategy. But what should Meijer do? • The answer is also clear, if Meijer understands Kroger's payoffs. Clearly Kroger will run the Deli special, so it only makes sense for Meijer to run the meat special. • This is the Nash equilibrium -- what do we mean by equilibrium formally? • Theequilibrium or anticipated strategies are those strategies for which for every player, given the choice of strategies of the other players, can not increase his payoff.

27. What is the equilibrium in Game 5?

28. Rule 3: After eliminating dominated strategies and not having dominant strategies, choose as your strategy the equilibrium strategy.

29. C. Applications of Simultaneous Move Games to Firm Strategy: Quantity v. Price Competition • Cournot Equilibrium • Model: 2 firms (1 & 2); Homogenous Product; Constant Marginal Cost • Firm Strategy: Choose output to maximize π believing that the other firm does not change its Q if you change yours. • Results: • 1) Firm has downward sloping demand. • 2) Price > MC in equilibrium • 3) Price < PM (the monopoly price) • 4) Firm's demand curve becomes more elastic as the # of firms increases. • 5) Price decreases as # of firms increases.

30. Query: Will equilibrium be at Price = MC = 1? Will output be 20, with 10 produced by each firms?

31. MR1 D1 Q2=10

32. Q2 = 6.67 Q1 =6.67

33. Reaction Function • The reaction function for a player (firm) is the best (profit-maximizing) response (output) given the action (output) of the other player (firm) • In this example we have • Q1 = 10 - Q2/2 • Q2 = 10 - Q1/2 • How do we get this? • Inverse Demand Curve is P=21-Q1 = Q2 • MC = 1 • Firm 1’s profit is PQ1 - MC1Q1= • (21-Q1-Q2)Q1 - Q1 = 21Q1 - Q12 - Q1Q2 - Q1 • Then profit-maximization implies: • d1/dQ1 = 21 -2Q1 - Q2- 1 = 0 or Q1 = 10 - Q2/2

34. Cournot 1’s Reaction Equilibrium 2’s Reaction

35. Price (Bertrand) Competition • Suppose that firms compete (set) prices not quantity -- does it make a difference? • What does competing in prices mean? • Set a price and sell to all willing to buy at that price

36. Price Competition (continued) • Consider price competition as a game where you can set above or below your opponent. • Consider for a P > MC

37. What’s equilibrium? • P =MC for both firms.

38. Lesson • Avoid price competition. If products are homogenous, then set production and sales if possible.

39. P P- RP RP- D Q Q/2

40. Differentiated Products • Can not set quantity -- you meet all demand • Hhow can you reduce the competitiveness of price competition? • Product Differentiate • create some monopoly power. • Key: product differentiation means that small changes in prices will not lead to capturing entire market and tremendous gains in profits. • If quantity competition is not possible, differentiate your product to avoid direct price competition.

41. 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.

42. 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.

43. Cournot vs. Stackelburg

44. 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. • This is a form of collusion, since it is agreed that firms won't undercut. • 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

45. Pricing with a Dominant Firm P* DD MRD Q*

46. 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

47. 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.

48. 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

49. 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

50. 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.