Game Theory: Inside OligopolyPertemuan 19 - 20 Matakuliah : J0434/EKONOMI MANAJERIAL Tahun : 2008
Managerial Economics & Business Strategy Chapter 10 Game Theory: Inside Oligopoly
Overview I. Introduction to Game Theory II. Simultaneous-Move, One-Shot Games III. Infinitely Repeated Games IV. Finitely Repeated Games V. Multistage Games
Elements of Games • Environment • Rules • Players • Strategies • Payoffs
Some Possible Game Structures • 0-sum vs. variable sum • co-operative vs. non-cooperative • simultaneous mover vs. alternating mover
Important Strategic Considerations • Credible vs. non-credible threats (strategies) • Equilibria: • Nash • Sub-game Perfect
Normal Form Game(Simultaneous Movers - Prisoner’s Dilemma) • Environment - Police station after a crime wave. Police have evidence on a minor crime. Police have insufficient evidence on major crime • Players - Bonnie and Clyde • Rules - no escape is possible • Strategies - Rat or not rat • Payoffs - • No one rats: both get 3 years • One rats and the other stays quiet: rat gets 1 year, Silent partner gets 23 years • Both rat: both get 16 years
Resolving Bonnie & Clyde • If Bonnie Rats and • Clyde doesn’t rat, then Bonnie gets 1 year • Clyde rats, then Bonnie gets 16 years • If Bonnie doesn’t Rat and • Clyde doesn’t rat, then Bonnie gets 3 years • Clyde rats, then Bonnie gets 23 years • If Clyde Rats and • Bonnie doesn’t rat, then Clyde gets 1 year • Bonnie rats, then Clyde gets 16 years • If Clyde doesn’t Rat and • Bonnie doesn’t rat, then Clyde gets 3 years • Bonnie rats, then Clyde gets 23 years
The Normal Form of Prisoner’s Dilemma Bonnie 16,16 1, 23 Clyde 23,1 3,3
A Market Share Game • Two managers want to maximize market share (0-sum game) • Strategies are pricing decisions • Customers move to low priced product • Limits? • Capacity • Loyalty • Heterogeniety and preferences • Simultaneous moves • One-shot game
The Market-Share Game in Normal Form Manager 2 Manager 1
Key Insight: • 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.
No and multiple equilibria • Not all games will have a single equilibrium • Scissors, rock, paper • Battle of the Sexes
Player 2 Player 1 Child’s play
Gain Coordination in a non-cooperative environment • Find a coordinating device • Repeat the game finitely • Repeat the game infinitely using • Grim-trigger strategy • Tit-for-tat strategy
Developing a Coordination Device • Environment - Pulling groceries to market. Pulling harder yields higher gross revenues. Effort costs • Players - Mack and Myer • Rules - ? • Strategies - Pull or Shirk • Payoffs - • No one pulls, each nets $15 • One pulls and the other shirks, puller nets $10, shirker nets $35 • Both pull, each nets $25
Mack Myer Mack & Myer’s Game 25,25 10, 35 35,10 15,15 Nash? Payoffs?
Developing a Coordination Device • Solution is to hire an enforcer • Pay the enforcer $5 each to hit anyone who shirks. • Hospitalization costs $15 Mack 20,20 5, 15 Myer 15,5 -5,-5 Nash? Payoffs? Damage?
Examples of Coordination Games • Industry standards • size of floppy disks • size of CDs • industry organizations – UAW, ABA, etc. • National standards • electric current • traffic laws • HDTV
An Advertising Game • Two firms (Kellogg’s & General Mills) managers want to maximize profits • Strategies consist of advertising campaigns on three levels • Punishment for non-cooperation? • Credible punishment?
Equilibrium to the One-Shot Advertising Game General Mills Kellogg’s Nash Equilibrium
Can collusion work if the game is repeated 2 times? General Mills Kellogg’s
By backwards induction • In period 2, the game is a one-shot game, so equilibrium entails High Advertising 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 Advertising 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 firms play the game each year, forever? • Consider the following “grim-trigger strategy” by each firm: • “Don’t advertise, provided the rival has not advertised in the past. If the rival ever advertises, “punish” it by engaging in a high level of advertising forever after.” • 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. • Is this a credible threat?
Profits in an infinitely repeated game • Suppose we cooperate forever, then: • Suppose we play non-cooperatively forever after, then: • Suppose we cheat once, then we receive:
Profits in an infinitely repeated game • Cheat only if it is profitable to do so:
General Mills Kellogg’s Suppose General Mills adopts this trigger strategy. Kellogg’s profits? VCooperate = 12(1+i)/i Vnon-coop = 2/i pcheat = 20
Kellogg’s Gain to Cheating: pCheat - pCoop = 20 - 12 pcoop - pnon-coop = 12 - 2 8/10 > 1/i If i > 1.25 or 125% interest rate General Mills Kellogg’s
Key Insight • 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
Real World Examples of Collusion • Garbage Collection Industry • OPEC • NASDAQ • Airlines
2. OPEC • Cartel founded in 1960 by Iran, Iraq, Kuwait, Saudi Arabia, and Venezuela • Currently has 11 members • “OPEC’s objective is to co-ordinate and unify petroleum policies among Member Countries, in order to secure fair and stable prices for petroleum producers…”(www.opec.com) • Cournot oligopoly (quantity-based competition) • Absent collusion: PCompetition < PCournot < PMonopoly
Cournot Game in Normal Form Venezuela Saudi Arabia
One-Shot Cournot (Nash) Equilibrium Venezuela Saudi Arabia
Repeated Game Equilibrium* Venezuela • (Assuming a Low Interest Rate) Saudi Arabia
OPEC’s Demise Low Interest Rates High Interest Rates
Caveat • Collusion is a felony under Section 2 of the Sherman Antitrust Act. • Conviction can result in both fines and jail-time (at the discretion of the court). • OPEC isn’t illegal; US laws don’t apply • DeBeers?
U.S. Law • Sherman Antitrust Act • Section 1 Every contract, combination in the form of a trust or otherwise, or conspiracy , in restraint of trade or commerce ... is hereby declared to be illegal. • Section 2 Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any person or persons, to monopolize any part of the trade or commerce among the several states, or with foreign nations, shall be deemed guilty of misdemeanor ...
U.S. Law • Clayton Antitrust Act • Section 2 [I]t shall be unlawful for any person engaged in commerce ... to discriminate in price between different purchasers of commodities of like grade and quality ... where the effect of such discrimination may be substantially to lessen competition or tend to create a monopoly ... • Section 3 It shall be unlawful ... to lease or [sell] goods ... on the condition, agreement, or understanding that the lessee or purchaser thereof shall not use or deal in the goods ... of a competitor or competitors of the lessor or seller, where the effect ... may be to substantially lessen competition or tend to create a monopoly in any line of commerce. • Section 7 [N]o corporation engaged in commerce shall acquire ... the whole or any part of the stock or other share capital ... of another corporation engaged also in commerce, where ... the effect of such acquisition may be substantially to lessen competition, or tend to create a monopoly ...
U.S. Law • Federal Trade Commission Act • Section 5(a)(1) Unfair methods of competition in or affecting commerce, and unfair or deceptive acts or practices in or affecting commerce, are hereby declared unlawful. • Munn v. Illinois • Clothed in public interest • Subject to regulation
Alternating Mover Games • One player acts then the other reacts • Look forward, reason backward • Sub-game perfect equilibrium (SPE) • New elements • Information node • Information set • Order of play
Pricing to Prevent Entry: An Application of Game Theory • Two firms: an incumbent and potential entrant • The game in extensive form:
10, 10 No Price War Incumbent Enter Price War Entrant -20, -10 0, 30 Don’t Enter The Entry Game in Extensive Form
Divide into Sub-games(each node) 10, 10 No Price War Incumbent Enter Price War Entrant -20, -10 0, 30 Don’t Enter
Solve Each Sub-game 10, 10 No Price War Incumbent Enter Price War Entrant -20, -10 0, 30 Don’t Enter
One Subgame Perfect Equilibrium 10, 10 No Price War Incumbent Enter Price War Entrant -20, -10 0, 30 Don’t Enter
Pricing to Prevent Entry • Suppose you want to fight a war to create a reputation? • What’s the price of the reputation? • What’s the gain? • Suppose you want to buy out the entrant? • What is an acceptable price? • What is an affordable price? • What sort of dynamic does this create?
Technology Adoption • 2 firms • Alternating movers
70, 40 Follower 100, 30 Leader 50, 30 Follower 80, 40 Technology Adoption Adopt Adopt Not Adopt Adopt Not Adopt Not Adopt