Game Theory: Inside Oligopoly Pertemuan 19 - 20 Matakuliah : J0434/EKONOMI MANAJERIAL Tahun : 2008 Game Theory: Inside Oligopoly Pertemuan 19 - 20

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

Child’s play Player 2 Player 1

Multiple Equilibria - Battle of the Sexes Him Her

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’s Game Mack Myer 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:

Suppose General Mills adopts this trigger strategy. Kellogg’s profits? VCooperate = 12(1+i)/i Vnon-coop = 2/i pcheat = 20 General Mills Kellogg’s

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 Saudi Arabia (Assuming a Low Interest Rate)

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 Munn v. Illinois 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:

The Entry Game in Extensive Form Entrant Don’t Enter Enter Incumbent No Price War Price War 10, 10 -20, -10 0, 30

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

Technology Adoption 70, 40 100, 30 50, 30 80, 40 Leader Follower Adopt Not Adopt Adopt Not Adopt Not Adopt

Technology Adoption 70, 40 100, 30 50, 30 80, 40 Leader Follower Adopt Not Adopt Adopt Adopt Not Adopt Not Adopt

Technology Adoption with different timing Leader Follower

Uncertainty and the first-mover advantage First-mover advantage is the gain associated with being first Market foreclosure Customer loyalty Examine information that is available.

Uncertainty and the first-mover advantage in capacity choice 12, 6 4, 9 6, 4 -12, -10 -15, 4 3, 2 5, 3 10, 8 Leader Follower Low Demand Case High Large Small

Uncertainty and the first-mover advantage in capacity choice Large 10, 8 Large Follower High Demand Case Small 12, 6 Leader Large 4, 9 Small Follower 6, 4 Large -12, -10 Large Follower Low Demand Case Small -15, 4 Leader Large Small 3, 2 Follower Small 5, 3

Uncertainty and the first-mover advantage in capacity choice Large 10, 8 Large Follower High Demand Case Small 12, 6 Leader Large 4, 9 Small Follower 6, 4 Large -12, -10 Large Follower Low Demand Case Small -15, 4 Leader Large Small 3, 2 Follower Small 5, 3