Lecture 7. Oligopoly Market (oligopoly market)
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1. Overview
2. Price leadership model
3. Cartel model
4. Bertrand model
5. Kinked demand curve model
6. Cournot model
7. Bertrand model with differentiated products
8. Hotelling model
9. Hotelling model with location choice
10. Stackelberg model
11. Entry deterrence model
1. Overview
(1) Definition
① Oligopoly market: A market with a small number of firms (e.g., tennis balls, cigarettes)
○ Type 1. Independent behavior of each firm
○ Type 2. Tacit collusion → price leadership model
○ Type 3. Full collusion → cartel○ In the real world, most markets are oligopolies: because other market theories did not fit reality well, funding for economics had been decreasing before oligopoly theory was developed.
③ (Related concept) Perfectly competitive market (perfect competitive market) (e.g., agricultural products, milk)
④ (Related concept) Monopoly market (monopolistic market) (e.g., water supply, cable TV)
⑤ (Related concept) Monopolistic competition (monopolistic competitive market) (e.g., novels, movies)
(2) Characteristics of an oligopoly market
① Market price is greater than marginal cost: differs from perfect competition where P* = MC(q*).
② Each participant’s actions affect the market price: differs from monopoly where there is only one participant.
③ Oligopoly output: more than monopoly, less than perfect competition.
④ Oligopoly price: lower than monopoly, higher than perfect competition.
⑤ As the number of firms increases, the oligopoly approaches perfect competition.
(3) Herfindahl–Hirschman Index (HHI)
① If three firms have market shares 60%, 25%, and 15%:
60^2 + 25^2 + 15^2 = 4,450
② U.S. Department of Justice guideline:
○ HHI ＜ 1,500: highly competitive market
○ 1,500 ＜ HHI ＜ 2,500: moderately competitive market
○ 2,500 ＜ HHI: oligopoly
○ If HHI exceeds 1,500, mergers that significantly increase HHI may be subject to special investigation and may be blocked.
③ HHI of some oligopoly industries (Sources: ref1, ref2, ref3, Neilson, Reuters, Forbes, Edmunds Auto)
○ PC microprocessors: 6,190; Intel, AMD
○ Aircraft: 5,008; Boeing, Airbus
○ Operating systems: 4,809; Windows, macOS, Linux
○ Smartphone operating systems: 4,326; Android, Apple
○ Warehouse clubs: 3,730; Costco, Sam’s Club
○ Game consoles: 3,706; Nintendo, Xbox, PlayStation
○ Mobile carriers: 2,768; Verizon, AT&T, Sprint, T-Mobile
○ Tablet PCs: 2,306; Apple, Samsung, Amazon, Asus
○ Diamonds: 2,029; De Beers, ALROSA, Rio Tinto
○ Automobiles: 1,131; GM, Ford, Toyota, Chrysler, Honda, Nissan
2. Price Leadership Model (price leadership model)
(1) A form where one firm sets the price and other firms follow it: a tacit-collusion regime.
(2) Example 1. Jinyang Benz flyer advertisement
① An ad stating that if you bring a competitor’s flyer showing a lower price than theirs, they will refund twice the price difference.
② A kind of chicken game—rather than the peak of price destruction, it functions as an invitation to tacit collusion.
3. Cartel Model (cartel model)
(1) A regime of full collusion.
(2) Example: the oil cartel OPEC (Organization of the Petroleum Exporting Countries)
4. Bertrand Model (Bertrand model)
(1) Definition: an imperfect competition model where price is the strategic variable (often used when it is difficult to adjust output).
① Di denotes the demand faced by firm i.
② pi means firm i sets price pi as its strategy.
③ p-i means the other firms (1, 2, ···, i-1, i+1, ···, n) set prices p1, p2, ···, pi-1, pi+1, ···, pn as their strategies.
④ For simplicity, consider only i = 1, 2.
⑤ Each firm takes the rival’s price as given and chooses its own price: game theory applies.
(2) Payoff
(3) Nash equilibrium condition: the strategy profile (p1, p2) must satisfy the following.
① Proposition 1. (c, c) is one Nash equilibrium.
② Proposition 2. (c, c) is the unique Nash equilibrium.○ There exists i such that pi ≤ p-i.
○ Case 1. c ＞ pi: firm i’s profit is negative, so pi = c is better (not a Nash equilibrium).
○ Case 2. c ＜ pi: if the other firm sets p-i = pi − ε, the other firm’s profit improves (not a Nash equilibrium).
○ Case 3. c = pi ＜ p-i: if c ＜ pi ＜ p-i, firm i’s profit becomes positive.
5. Kinked Demand Curve Model (kinked demand curve)
(1) Like the Bertrand model, it assumes firms compete via price.
Figure 1. Kinked demand curve model
(2) Demand curve
① If a firm raises its price, rivals keep the current price: quantity demanded drops sharply when price increases.
② If a firm cuts its price, rivals also cut their prices: quantity demanded does not rise much when price decreases.
(3) Marginal revenue curve: explains why firms in reality do not change prices often.
① The marginal revenue curve becomes discontinuous in the middle, so within the discontinuity range the gain from changing the market price is not large.
② The side effects from changing prices can be larger.
6. Cournot Model (Cournot model, Qournot model) : also called “Kurnoh / Cournot” model
(1) Overview
① Definition: an imperfect competition model where quantity (output) is the strategic variable (often used when it is difficult to change price).
② Each firm takes the rival’s output as given and chooses its own output: game theory applies.
(2) Payoff
(3) Profit maximization problem
① BRi: best response of firm i
② BRi(q-i): firm i’s best response when the other firms’ outputs (1, 2, ···, i-1, i+1, ···, n) are fixed
(4) Nash equilibrium: also called Cournot equilibrium
(5) Conclusion
7. Bertrand Model with Differentiated Products
(1) Definition: Products are not identical (not homogeneous), but demand for one product affects demand for the other.
① qi: demand faced by firm i
② qi(pi, p-i): demand faced by firm i when firm i’s price is pi and the other firm’s price is p-i
③ Example: Samsung Galaxy phone vs Apple iPhone
(2) Payoff
(3) Profit maximization problem
(4) Nash equilibrium
8. Hotelling Model
(1) Overview
① Definition: for 0 ≤ a＜b ≤ L, consumer location ℓ, and seller location i
② (Note) Distance does not have to be literal physical distance.
③ If there are two sellers, the consumer location that yields equal utility from purchasing from either seller is as follows.
(2) Demand for sellers at a and b
(3) Payoff
(4) Profit maximization problem
(5) Nash equilibrium
9. Hotelling Model with Location Choice
(1) Situation: a slightly modified version of the Hotelling model
① Stage 1. Two firms choose locations a and b.
② Stage 2. After observing the other firm’s location, each firm chooses its product price pa and pb.
③ Using backward induction, one can find the Nash equilibrium.
(2) Stage 2: This Nash equilibrium has already been covered in the Hotelling model.
① a: captive customers of the firm located at a
② L-b: captive customers of the firm located at b
③ Meaning: pb − pa is proportional to the difference in the number of captive customers and proportional to the distance between the two firms.
(3) Stage 1: Each firm must choose a and b that maximize its payoff.
① Conclusion 1. If firms can choose only locations on the beach, firm a should locate at the far left (ℓ = 0).
○ demand effect
○ price effect: by the Stage 2 Nash equilibrium condition, the price effect should be 0
○ strategic effect
○ Since the change in payoff with respect to increasing a is negative, a should be the smallest, 0
② Conclusion 2. If firms can choose only locations on the beach, firm b should locate at the far right (ℓ = L)
③ Conclusion 3. If firms can choose locations outside the beach, the following solution becomes the Nash equilibrium.
10. Stackelberg Model (Stackelberg model)
(1) Situation: a slightly modified version of the Cournot model
① Condition
② Stage 1. Firm 1 is the leader (1st mover): firm 1 chooses its output q1
③ Stage 2. Firm 2 is the follower: after observing q1, firm 2 chooses its output q2
④ Using backward induction, one can find the Nash equilibrium.
(2) Stage 2
(3) Stage 1
(4) Conclusion
① The Nash equilibrium outputs q1* and q2* are as follows.
② Leader’s advantage: compared to the Cournot model, firm 1 earns more and firm 2 earns less.
③ (Note) Depending on how the problem is set up, the follower may also gain.
11. Entry Deterrence
(1) Situation: a slightly modified version of the Stackelberg model
① Condition
② Stage 1. Firm 1 chooses output q1
③ Stage 2. After observing q1, firm 2 decides whether to enter the market: entry cost is K2
④ Stage 3. If firm 2 enters, it chooses output q2
⑤ Using backward induction, one can find the Nash equilibrium.
(2) Case 1. K2 = 100
① Stage 3
② Stage 2. Derive the condition under which firm 2 enters.
③ Stage 1. Compare the three cases.○ case 1. q1 ＜ 100: firm 2 enters
○ case 2. q1 = 100: firm 2 may enter or may not enter (π1 graph has a discontinuity)
○ case 3. q1 ＞ 100: the lower q1 is, the better○ Therefore, (q1, q2) = (100, 0) is a Nash equilibrium, and firm 2’s entry is deterred in this case.
○ In case 2, because there are two possible outcomes, it is better to set q1 slightly greater than 100.
(3) Case 2. K2 = 64
① Stage 3
② Stage 2. Derive the condition under which firm 2 enters.
③ Stage 1. Compare the three cases.○ case 1. q1 ＜ 104: firm 2 enters
○ case 2. q1 = 104: firm 2 may enter or may not enter (π1 graph has a discontinuity)
○ case 3. q1 ＞ 104: the lower q1 is, the better○ Therefore, (q1, q2) = (60, 30) is a Nash equilibrium; in this case firm 1 accommodates entry and compromises on q1.
Entered: 2020.05.05 22:55