Strategic Pricing

1. 1 Strategic Pricing How to price in a game with competitors

2. 2 Oligopoly Oligopoly = Competition between multiple firms (still assuming mass market of buyers) Assume number of firms is fixed No immediate threat of entry Base-case: homogeneous firms Production technologies identical (i.e., same cost structure) Products identical (i.e., same demand curve) Types of competition Price competition Quantity competition Extensions Product differentiation Tacit collusion

3. 3 Class Experiment High or Low Production?

4. 4 The Production Game Players: approximately 76 of you Choices Capacity = 2 units Choose 0, 1 or 2 units Payoffs No production costs Price = 160 � Total Production Quantity Profit = Price x Quantity

5. 5 Competition in mass markets with homogenous products What happens when firms compete in quantity? What happens when firms compete in price?

6. 6 Price vs. quantity competition Monopoly Firm can choose quantity or price Same answer either way Oligopoly Firms can still choose quantity or price Now, however, this matters Different models Different conclusions The key is capacity The price-competition model assumes all firms have sufficient capacity to serve the entire market The quantity-competition model is identical to the price competition model with the addition of capacity constraints So, the quantity competition model is good for situations in which firms are able to commit to production limitations (e.g., via capacity choices) We will see that For the same number of firms, price competition results in lower industry profits As the number of firms increases, profits under quantity competition converge to those under price competition (i.e., due to the more intense competition)

7. 7 Tough price competition

8. 8 Tough Price Competition CD ROM phonebooks 1986: Nynex charged $10,000 per disk for NY directory ProCD and Digital Directory Assistance Workers in China at $3.50 daily wage Outcome similar to �Perfect� competition Charge $200 each Price forced down to marginal cost

9. 9 Same market assumptions as before

10. 10 Competition in prices Firms post prices simultaneously, afterwards see what they sell P1 and Q1 denote F1�s price and quantity, respectively P2 and Q2 denote F2�s price and quantity, respectively Here, price is the choice variable, quantity is the outcome variable Goods are perfect substitutes (ex: flour, sugar). Consumers buy from the firm with lowest price(provided price is less than their WTP) If firms set different prices, the low-price firm gets 100% share(implicit capacity assumption: both firms can supply entire market) If firms set identical prices, firms get equal market shares This is known as the �Bertrand� model of oligopolistic competition

11. 11 Informal analysis Suppose F1 believes that F2 will maintain price Assume the firms begin with identical prices of $600 At this price, 400 customers buy (note: same as monopoly case) Firms Split the market (since prices are equal), 200 units each Have identical profits of ($600 � $200)200 = $80k(note: split the monopoly profit level) If F1 lowers the price a little, say to $590, it gets 100% market share No one buys from F2 (if price stays at $600) F1 gets Q1 = 1000 � 590 = 410 in sales (from demand equation) Profits are (590 � 200)410 = $159,900 for F1 0 for F2 F1 wants to do this (ideally, cut price by 1 cent!)

12. 12 Nash equilibrium? It is not realistic for F1 to believe that F2 will maintain price What is true for F1 is also true for F2 If F1 cuts price a little, F2 loses everything Therefore, F2 will also cut price to match, if not exceed, F1�s cut Each firm�s reaction to a price cut is to cut price � where does it stop? To solve, use Nash equilibrium: posted prices are stable when neither firm wants to change given competitor�s price If firms charge different prices, the high priced firm wants to switch to a lower price, so prices must be equal If common price above marginal cost, both firms prefer to shave price to gain 100% share, so price must be less than or equal to MC If common price is less than marginal cost, both firms prefer to exit the market and sell nothing at all, so price must equal MC

13. 13 Outcome of pricing game Each firm has a marginal cost of $200 So, both price at $200 Quantity sold is 1000 � 200 = 800 units Each firm gets 50% share (400 units) Neither firm makes a profit This is an insidious outcome, neither firm can raise price without risking entire loss of share Actually, it�s worse than that �

14. 14 Price trap with no exit Since both firms earn 0 profit, each is indifferent to exiting But, is it a Nash equilibrium for one to exit If one firm exits, the other charges the monopoly price ($600 is the best reply of the remaining firm to a competitor that stays out) But, if one firm stays and charges $600, the other firm wants to enter and charge slightly less This cannot be a stable situation (Nash equilibrium) Besides, who would �volunteer� to leave? It is only Nash for both firms to post P = MC Otherwise, either someone wants to enter Or, someone wants to cut price

15. 15 Usual objection But won�t each firm realise that if it cuts its price the other firm will follow? (hold that thought�we�ll address soon)

16. 16 Fixed costs, exit and entry Outcome is P = MC No fixed costs are covered If firms have no fixed costs, they earn zero profits If they have fixed costs, they have losses In the long run, firms w/fixed operating costs must exit Question is: what happens then? If entry is free, price competition happens all over again (as discussed on previous slide) If entry is costly, no entry occurs The moment an entrant comes in, prices drop to MC Incumbent earns monopoly profit because the threat to cut price to MC is credible in this situation (i.e., it is a Nash equilibrium) This is why it may be rational for firms to try to hold out Need to be careful using this reasoning � if it is rational for you to hold out, it is probably rational for your competitor to do so as well Amazon.com investors will never get a positive return on their investment Better: differentiate your product

17. 17 Softer, quantity competition

18. 18 Competition in quantities Firms simultaneously choose quantities, afterwards see prices Think of this as choosing capacities Q1 denotes F1�s quantity Q2 denotes F2�s quantity The market-clearing price is P Here, quantity is the choice variable, market price is the outcome variable Again, goods are perfect substitutes (ex: flour, sugar). However, there may not be enough capacity to serve entire market Since products are identical, prices are identical Capacity limitations imply higher market-clearing prices than price competition This is the �Cournot� model of oligopolistic competition

19. 19 Informal analysis Assume the firms begin with identical capacities of 200 To sell all their product (400 units, total), market price is $600 (again, same as monopoly case) Firms have identical profits of ($600 � $200)200 = $80k(split the monopoly profit level) Suppose F1 believes that F2 will maintain capacity What capacity should F1 choose? A partial schedule of outcomes is

20. 20 F1�s �residual� demand curve Preceding table shows F1�s demand when F2 maintains quantity/capacity It is D1 = 800 � Q1 (just subtract Q2 = 200 from market demand schedule)

21. 21 F1�s reaction curve The preceding analysis can be done for any quantity choice by F2 This results in a schedule of best responses for F1 given any Q2

22. 22 Equation of the reaction curve F1�s MR when F2 chooses Q2 is MR = (1000 � Q2) � 2Q1 So, if MR = MC: (1000 � Q2) � 2Q1 = 200 Rearranging terms: Q1 = 400 � � Q2

23. 23 Nash equilibrium F2 also has a reaction curve, which can be plotted along with F1�s Nash equilibrium is the point of intersection: both firms best reply

24. 24 Outcome of pricing game Each firm chooses capacity of: 800/3 ? 267 Market price is: 1000 � 1600/3 ? $467 Each firm has profit = (467 � 200)267 = 71,200k Much better outcome than price competition Not quite as good as sharing monopoly profit Firms would prefer to collude and profit more This is illegal Even if it weren�t, how would firms prevent cheating? At quantities of 200, both want to produce more Check the reaction curves!

25. 25 MR in Monopoly vs. Cournot

26. 26 The 2 components of MR To sell one more unit, you have to Must sell to someone with lower WTP ? price drops This drops price to currently buyers If monopolist is selling 400 and wants to sell 401, she must lower the price on 400 units Under Cournot, only consider effect on units YOU sell If firms sell 200 each, lower price effects you only through your existing 200 customers When making decisions, you don�t care what happens to competitor�s profits Less downside for you (MR falls slower) You are more inclined to cut price (have more capacity)

27. 27 Now, the general 2-firm Cournot case Demand: P = a � bQ where a and b are constants and Q = (Q1 + Q2) is the market quantity Firms have identical, constant marginal costs = C F1 profit maximized where MR1 = MC1 TR1 = PQ1 = (a � bQ1 � bQ2)Q1 = (a � bQ2)Q1 � bQ12 MR1 = ?TR/?Q1 = (a � bQ2 ) � 2bQ1 Setting MR = MC: (a � bQ2 ) � 2bQ1 = C Rearranging terms gives reaction function for F1: Since the firms are symmetric the reaction function for F2 is identical Solving two equations in two unknowns (use substitution as before) Check this against the results in our example (and use it for problems!)

28. 28 The general n-firm Cournot case Keep the general case assumptions but assume there are n firms Nash equilibrium solution procedure the same But now there are lots of simultaneous reaction functions to deal with It can be shown that the amount produced by each firm i is The interesting thing is that the market price is So, as n ? infinity, P* ? C [because a/(n+1) ? 0 and n/(n+1) ? 1] In the limit, the same result as price competition! In mass, homogenous-good markets with lots of small competitors, firms earn zero profit

29. 29 Competition in quantities = �Cournot� 2 Possible scenarios: Quantity decisions have to be made a long time before sale Firms choose the quantity they want to produce without knowledge of others� choices After supply is determined, there is a �market mechanism� that finds the price at which Demand equals that available Supply Firms can limit their capacities Firms choose their capacity without knowledge of others� choice of capacity Once they see each others� capacity, they each charge the market clearing price

30. 30 The Role of Tough Commitments

31. 31 Quantity Pre-commitments Reaction curves are downward sloping The more F1 expects F2 to produce, the less F1 wants to produce F2 should pre-commit to producing more than it would otherwise want to Example: Investing in mass-production equipment Such pre-commitments cause rivals to back off and �accommodate� by producing less When are quantity increases credible? Reputation for high quantity Large supply or purchase contracts Cost leadership: investments in lower unit production costs Irreversible capacity investments

32. 32 Tough quantity competition

33. 33 Pre-commitments A tough commitment means that F2 wants to produce more, at every output level of F1�s: the best response curve is shifted up. The commitment moves the equilibrium from A to B. CAREFUL! The commitment is only worth it if the firm earns more at B (after paying for the commitment) ? you have to check.

34. 34 Pre-Emption Commitments change the game: now one or the other will try to commit Either firm may commit... But what happens if you can commit first? Other firm observes your action before choosing their own: ?You gain a first-mover advantage

35. 35 Case: Memory Chips Early 1980s: market dominated by US firms mid 1980s: Japanese firms (Toshiba, NEC) increased their investment in new capacity (while US firms didn�t) late 1980s: 80% of market controlled by Japanese firms 1990s: massive investments by South Korean firms (Samsung, Hyundai) while the Japanese firms have not invested

36. Commitment and choosing capacities: If capacities have to be chosen simultaneously, choose to build a plant whose capacity = Cournot quantity BUT If one firm can choose capacity first, and can make sure the other firm sees its choice: The second firm to build will choose its �best response� to the first firm�s capacity The first firm can profit by making a tough commitment in capacities: build a large plant Both firms want to be first There may be a �race� to build first

37. 37 Pre-emptive capacity building If firms were building at the same time, F2 would build a plant with capacity equal to the Cournot quantity Qc But if F2 builds first, it will build a larger capacity Q2

38. 38 Strategies to dampen competition

39. 39 Return to price competition Even with only two firms P = MC This is a very bad position in which to find yourself What can be done? Try to change the game! Merge (and earn monopoly profits) Differentiate your products (a common solution) Obtain a cost advantage (see Gans, p. 148 � 151) Collude (illegal and, in any event, hard to make work)

40. 40 Niche market differentiation Go back to price (Bertrand) competition example Assume buyer demand is horizontal at $1000(perfectly elastic) Suppose F1 can alter the design of its product The new product appeals to 40% of the market These customers are willing to pay a $50/unit premium for this product MC of this product is $225 ($25 more expensive) Old product must be retired

41. 41 Analysis F1 wishes to go to the new design Under old design, P1 = MC = 200 With new design, F1 can post P1 = 250 400 units sold ?1 = (250 � 225)400 = 10,000 What is F2�s best response? Since P1 > 200, F2 can post P2 > 200 as well For example, P2 = 201, ?2 = (201 � 200)600 = 600 What is Nash equilibrium? P2 = 201 ? P1 = 251 So this is not Nash

42. 42 Equilibrium in niche markets Calculating Nash is beyond the scope of this class Instead, look for undercut proof outcome Price difference must be $50, Any more and the 400 customers switch to F2 Any less and F1 could earn more by raising price F1 must earn same or more profit as what could be obtained by undercutting P2 slightly If P2 > 200, F1 can always Keep the old product Set P1 slightly below P2 and Get 100% of the market So, P2 cannot be too high, otherwise this option will be preferred

43. 43 Compute the equilibrium The two requirements imply, respectively P1 = $50 + P2 (P1 � 225)400 = (P2 � 200)1000 Substitute first requirement into second P1 = 800/3 ? 267 P2 = 650/3 ? 217

44. 44 Cooperation Collusive Pricing: Can firms collude without communicating?

45. 45 Large Electric Turbine Generators 1950s: three producers of large electric turbine generators in the US GE, Westinghouse and Allis-Chambers Lots of profits: low rivalry, high entry barriers Seem to maintain high prices during the 1950s Subject of antitrust investigation But how did collusion take place when there was no evidence of communication (let alone an agreement)

46. 46 Celestial Coordination Competition on tenders from electricity utilities A formal solicitation of bids was released Based on the time of the formal document, each firm would consult the lunar calendar Days 1-17 of lunar month: GE would �own� the contract (high bid with others bidding higher) Days 18-25: Westinghouse�s turn Days 26 to 28: A-C�s turn Gave market shares of 60%, 30% and 10% respectively. Why did A-C put up with this? Couldn�t be taken to court for breaking a contract. That contract would be illegal.

47. 47 Tacit collusion When interactions occur over many periods, firms can implement a wide range of outcomes Stay with price competition example Assume game is repeated indefinitely Firms have discount rate r Best case for firms is to post monopoly price Split market Split monopoly profit Problem: strong incentive to cheat (shave price) Can this be overcome in repeated case?

48. 48 Collusive strategies Consider this dynamic strategy Set price = $600 (monopoly price w/P = 1000 � Q) If opponent�s price was $600 this period, set price = $600 next period If opponent�s price was not $600 this period, set price = $200 forever Both firms adopt this �grim trigger� strategy Does either wish to deviate?

49. 49 Can F1 deviate profitably? Assume F2 follows the previous strategy If F1 also follows the strategy It gets (600 � 200)200 = 80k forever So, the PV of following the strategy is 80k/r Instead, F1 can undercut If it posts P1 = 599, ?1 = (599 � 200)401 ? 160k But, in all following periods, P2 = 200 (by the strategy) The best response in those periods is P1 = 200 So, F1 gets ?1 = 0 forever following a deviation It is not profitable to deviate from the strategy when If firms are �sufficiently patient,� collusion can be sustained

50. 50 Cooperation in repeated interactions The previous type of result holds in most repeated situations That is, cooperation can be sustained in repeated transactions � even though there are incentives to act opportunistically By cooperating, firms split the best outcome profit By deviating, a firm gets the short-run benefit but, when cheating is detected, play enters a �punishment� phase Punishment in future periods more effective with low discount rates(cheater�s lost future benefits have greater value) There are many cases where �reputation� may be important Commitment issues (playing �tough� with entrants) Delivering high quality products (avoiding lemons problems) Delivering agreed upon effort in strategic alliances (no free riding) Even Prisoners� dilemma can be resolved

51. 51 Co-opetition: Commitments that Facilitate Collusion Most Favoured Customer Clause (MFC) Manufacturers of antiknock petrol additives (Du Pont, Ethyl) were brought before the US Federal Trade Commission for using MFCs. The seller will pay buyers the best price they pay to anyone. Commits to not offering selective discounts to attract customers from rivals Lowers the gain from cheating on price collusion. �Meet the competition� clauses With rebates, you find out quickly about cheating Commitment makes the price war more bitter Loyalty Programs harder to cheat by stealing customers from others You can read more about these in Coopetition.You can read more about these in Coopetition.

52. 52 Trigger price strategies In some environments, you can�t tell who has cheated: Several firms You don�t see how much they�ve sold Variable demand ? when your price falls, you don�t know if it�s because demand fell, or someone cheated. Results in this environment: We can�t collude at monopoly prices, because cheating is too tempting ? we have to charge mid-range prices There is a �trigger price�: if the price falls below this trigger, we all revert to competition for a few periods (=punishment), then we cooperate again.

53. 53 Tacit collusion If you can�t talk to each other, how do you agree on a price? Focal point = something people gravitate to If the firms are identical, and can sustain collusion at monopoly price, that seems like an obvious focal point But usually firms have different costs, slightly different products ? how do you coordinate? Or you might have to charge a mid-range price (as in trigger strategies) ? what price should you charge? How do you reach agreement? One tactic: Raise your price, hope the others follow Explains why it�s easier to coordinate on not cutting prices, than on raising prices (inflation is the customer�s friend!)

54. 54 Ethics of tacit collusion If customers are better off because of collusion, seems ethically defensible Ex: If firms compete Bertrand, one will leave the market, and the other will charge monopoly prices Customers are better off with two firms colluding, but only if they�re charging mid-range prices (rather than monopoly prices) �no price wars� But such cases are fairly rare What about in the other situations?

55. 55 Why do you need to know? Suppose you�re entering a market with 3 or 4 producers. If they�re competing with very similar products, that�s a pretty competitive market you would expect that prices won�t fall drastically when you enter the market You enter so long as your marginal cost is less than the going price. But if they�re colluding: The price could fall drastically after you enter, if they don�t collude with you, or if there are now too many players to sustain collusion The going price is not enough information How would you pick up whether they�re colluding? Prices that don�t change, when costs or demand changes In some mkts, occasional price wars when prices go way down.