Economic Environment of business

1. Economic Environment of business Lectures 3 and 4 Oligopoly and game theory

2. Market structures

3. I. Conditions for Oligopoly? II. Role of Strategic Interdependence III. Game theory IV. Profit Maximization in Four Oligopoly Settings Cournot Model Stackelberg Model Bertrand Model Part I: Overview

4. Relatively few firms, usually less than 10. Duopoly - two firms Triopoly - three firms … Barriers to entry are moderate The products firms offer can be either homogeneous or differentiated (colors, location, quality). Examples: Car manufacturers, supermarkets, airlines, hotels, construction companies, ready-to-eat cereals, telecom., etc. Oligopoly

5. Strategic Interaction • Your price (or quantity, or advertising, or quality, or R&D) decisions do affect the profits of the rival firms! • Likewise, what rivals do affects your profits We deal with these situations using a tool: Game Theory

6. An Example: Airlines competition KLM British Airways • Normal-form game: • Players • Strategies • Payoffs (1st number in cell refers to BA)

7. KLM British Airways Solution in dominant strategies Strategy 1 dominates another strategy 2 if Strategy 1 yields larger profit than strategy 2 regardless of the action taken by the rival firm. If all players have a dominant strategy, then the game has a solution in dominant strategies. {QBA = 64, QKLM = 64} is a solution in dominant strategies.

8. KLM British Airways Solution in dominant strategies • Payoff from the DSS {QBA = 64, QKLM = 64} is 4.1 for both players. • They could do better if they set 48. • Why don’t they cooperate?

9. Nash Equilibrium

10. KLM British Airways Nash equilibrium NE: Set of strategies such that no firm wants to change its strategy given what everyone else is doing. In a NE every firm plays a best-response, i.e., maximizes its profits given its (correct) beliefs about its rivals’ strategies. {QBA = 48, QKLM = 64} is a NE {QBA = 64, QKLM = 48} is also a NE

11. A pollution game: no NE (in pure strategies) Government Firm Mixed strategy equilibrium: G inspects 80 % of the times and F pollutes 37.5 % of the times. Government: Inspect: 0.375*5 + 0.625*4= 4.375 Not to inspect: 0.375*(-5)+0.625*10 =4.375 Firm: Pollute: 0.8*5 + 0.2*10= 6 Not to pollute: 6

12. Example mixed strategies

13. Penalty kick Strategies for player: left or right corner? Strategies for keeper: left or right corner? keeper player

14. Three classical models of strategic interaction Cournot model (due to Augustin Cournot, 1838) Bertrand model (due to Joseph Bertrand, 1883) Stackelberg model (due to Heinrich von Stackelberg, 1934)

15. A few firms produce goods that are either homogeneous (perfect substitutes) or differentiated (imperfect substitutes) Firms set output to maximize profit Interaction is for one period Each firm believes their rivals will hold output constant if it changes its own output (rivals’ output is viewed as given or “fixed”) Barriers to entry exist Cournot Model

16. Cournot Duopoly Model 2 firms Market demand is P=100-Q Firm i cost is C(q)=40q Firm i acts in the belief that firm j will put some amount qj in the market. Then firm i maximizes profits obtained from serving the residual demand: Residual demand is P=(100-qj)-qi P demand P=100-Q 100 100-qj Residual Demand P=(100-qj)-qi qj MC qi qi(qj) MRr

17. Cournot Model Max{(100-qj-qi)qi-40qi} defines best-response (or reaction) function: a schedule summarizing the quantity q1 firm 1 should produce in order to maximize its profits for each quantity q2 produced by firm 2. Products are (perfect) substitutes: an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product ( reaction functions are downward sloping). qj Firm i’s reaction Function qj* r1 qi* qiM qi

18. Situation where each firm produces the output that maximizes its profits, given the the output of rival firms No firm can gain by unilaterally changing its own output We look for a pair of outputs (q1* , q2* ) such that The output q1* maximizes firm 1’s profits, given that firm 2 produces q2* The output q2* maximizes firm 2’s profits, given that firm 1 produces q1* Neither firm has an incentive to change its output, given the output of the rival Beliefs are consistent: In equilibrium, each firm “thinks” rivals will stick to their current output -- and they do so! Cournot Equilibrium

19. q2 r1 Cournot (Nash) equilibrium q2M=30 r2 q1M=30 q1 Cournot Equilibrium iC=400 q2*=20 q1*=20

20. More efficient firms put more units in the market

21. 2 M=900 Profit Possibility Frontier A 2A=450 2C=400 C 1 1A=450 1C=400 M=900 Rationale for collusion

22. Types of collusion Cartel agreements: an ‘institutional’ form of collusion (also called explicit collusion or secret agreements) Unlawful (Sherman Act and Art. 85 Treaty of Rome) Requires evidence of communication Tacit or Implicit collusion: attained because firms interact over and over again and ‘find’ ‘natural’ focal points. This second type make things complicated for antitrust authorities

23. How can firms collude without explicit communication to coordinate actions? • Consider the Cournot model analyzed before. • Suppose now that firms interact in the market over an infinite number of periods • Then, the following “trigger strategy” by each firm is a Nash equilibrium: • Start producing qi=15 (half monopoly quantity) • Continue producing qi=15 period after period as long as the rival produces qj=15. If he/she deviates, then “punish” him by producing the Cournot quantity qi=20 forever. • In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods.

24. Cooperate = 450 +450/(1+r) +450/(1+r)2 + 450/(1+r)3 + … = 450 (1+1/r) Suppose firm 2 adopts this trigger strategy. Does it pay to deviate? Cheating = 506.25 +400/(1+r) + 400/(1+r)2 + 400/(1+r)3 +… = 506.25 +400/r When deviating, the best quantity is 22.5 (from the reaction function), and this yields a payoff of 506.25. It does not pay to deviate iff r < 0.8888

25. In period 2, the game is a one-shot game, so equilibrium entails “High Production” in the last period. This means period 1 is “really” the last period, since everyone knows what will happen in period 2. Equilibrium entails “High production” by each firm in both periods. The same holds true if we repeat the game any known, finite number of times. Can collusion work if interaction lasts just a few (2) periods? NO

26. Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: Ability to monitor actions of rivals Ability (and reputation for) punishing defectors Low interest rate High probability of future interaction Key Insight

27. Cartel founded in 1960 by Iran, Iraq, Kuwait, Saudi Arabia, and Venezuela Currently has 11 members (www.opec.org) “OPEC’s 11 members are all developing countries whose economies are heavily reliant on oil export revenues. They therefore seek stable oil prices that are fair and reasonable for both producers and consumers of oil.” Cournot oligopoly Absent collusion: PCompetition < PCournot < PMonopoly A real world example of Collusion: OPEC

28. Cournot GameOne-Shot Cournot (Nash) Equilibrium Venezuela Saudi Arabia

29. Repeated Game Equilibrium* Venezuela Saudi Arabia • (Assuming a Low Interest Rate)

30. OPEC’s Cartel Low Interest Rates High Interest Rates

31. Factors that favors the sustainability of tacit collusion  506.25 • In general anything that makes the green area more important than the red area. 450 400 Time Gains from deviating Losses from punishment

32. Collusion is more likely with fewer firms in homogeneous product markets with more symmetric firms in markets with no capacity constraints in very transparent markets (cheating is seen easily) no hidden discounts no random demand observability lags

33. Few firms Firms produce identical products at constant marginal cost. Each firm independently sets its price in order to maximize profits Barriers to entry Consumers enjoy Perfect information Zero transaction costs Bertrand Model

34. Firms set P1 = P2 = MC! Why? Suppose MC < P1 < P2 Firm 1 earns (P1 - MC) on each unit sold, while firm 2 earns nothing Firm 2 has an incentive to slightly undercut firm 1’s price to capture the entire market Firm 1 then has an incentive to undercut firm 2’s price. This undercutting argument continues... Equilibrium: Each firm charges P1 = P2 =MC Bertrand Equilibrium

35. Two firms are enough to eliminate market power If firms are symmetric, market power is eliminated entirely If firms are asymmetric, market power is substantially reduced Solutions: Capacity constraints Repeated interaction Product differentiation Imperfect information Bertrand Paradox

36. The “chicken” game 2 guys, cars aligned, first to turn: “coward,” “chicken” How to win this game? Commit, tie your hands “Burning the bridges” game 2 armies, advance or retreat: how to gain this game? By burning the bridges behind the army, a general converts the threat “I will not retreat” into credible. Stackelberg game Strategic Moves

37. Few firms Producing differentiated or homogeneous products Barriers to entry One firm is the leader The leader commits to an output before all other firms Remaining firms are followers. They choose their outputs so as to maximize profits, given the leader’s output. Strategic MovesStackelberg Model

38. Cournot: players threat each other “I will flood the market so you better don’t put many units in the market; otherwise the price will be too low.” Stackelberg: leader firm gets to move first and indeed floods the market; this strategic move confers a competitive advantage. Stackelberg game

39. Monopoly Output output Follower Leader Cournot Output The Stackelberg game in Extensive Form payoffs Solution: Subgame Perfect equilibriumSet of strategies constituting a Nash equilibrium in every subgame (stage)

40. Increasing Profits for Firm 1 1 = $100 1 = $200 Another look at Cournot decisions Q2 • Firm 1’s Isoprofit Curve: combinations of outputs of the two firms that yield firm 1 the same level of profit r1 B C A D Q1M Q1

41. Q2*  1 = $100  1 = $200 Q1* Another Look at Cournot Decisions: Q2 r1 Q1* =Firm 1’s best response to Q2* Q1M Q1

42. CournotEquilibrium Another Look at Cournot Equilibrium Q2 Firm 2’s Profits r1 Q2M Q2* Firm 1’s Profits r2 Q1M Q1* Q1

43. r1 Q1M Stackelberg Equilibrium Q2 Follower’s Profits Decline Stackelberg Equilibrium Q2* Q2S r2 Leader’s Profits Rise Q1* Q1S Q1

44. Stackelberg model illustrates how commitment can enhance profits in strategic environments Leader produces more than the Cournot equilibrium output Larger market share, higher profits First-mover advantage Follower produces less than the Cournot equilibrium output Smaller market share, lower profits Stackelberg Summary

45. Different oligopoly scenarios give rise to different optimal strategies and different outcomes Your optimal price and output depends on … Beliefs about the reactions of rivals Your choice variable (P or Q) and the nature of the product market (differentiated or homogeneous products) Your ability to commit to quantity Summary

46. Two managers want to maximize market share Strategies are pricing decisions Simultaneous moves One-shot game Application: A Market Share Game

47. The Market-Share Game in Normal Form Manager 2 Manager 1

48. Market-Share Game Equilibrium Manager 2 Manager 1 Nash Equilibrium

49. Game theory can be used to analyze situations where “payoffs” are non monetary! We will, without loss of generality, focus on environments where businesses want to maximize profits. Hence, payoffs are measured in monetary units. Key Insight:

50. Feature: Non-rivalry between the players. Industry standards size of floppy disks size of CDs quality standards (ISO). National standards electric current (110/220 volts) traffic laws (priority to the drivers on your right), etc. Application: Coordination Games