ECO 610401

1
ECO 610-401

• Monday, October 27th
• Market Structure Price and Output with Market
  Power (continued)
• Game Theory and Strategy Simultaneous Moves
• Readings Brickley et. al, Chapter 9251-263
• Hoyt, Lecture 61-13
• Monday, November 3rd
• Game Theory and Strategy Repeated Games,
  Credibility, and Collusion
• Readings Brickley et. al, Chapter 9264-273
• Hoyt, Lecture 613-19

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Market Structure Industry Competition
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Intensity of Rivalry among existing Competitors

• Intensity is greater when
• Numerous or equally balanced competitors
• Slow industry growth
• High fixed or storage costs
• Lack of differentiation or switching costs
• Capacity augmented in large increments
• Diverse goals of competitors
• High Stakes
• High Exit Barriers
• Specialized Assets
• Fixed Costs of Exit
• Strategic Interrelationships

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Market Structure and Equilibrium Price

• Game 3 Duopoly (price competition)
• 20 buyers with a reservation price
• Each buyers 1 unit
• Cant pay more than that, want to pay less
• 2 Sellers who can sell as much as they want at
  a (marginal) cost of 2 per unit
• Seller 1 picks price
• Buyers respond to price (note if they want to
  buy)
• Seller 2 can pick a price
• Buyers respond to price (note if they want to
  buy)
• continue until a seller is not willing to
  respond (change price)
• Then sales are made at that price

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Market Structure and Equilibrium Price

• Game 4 Duopoly (quantity competition)
• 20 buyers with a reservation price
• Each buyer 1 unit
• Cant pay more than that, want to pay less
• 2 Sellers who can sell as much as they want at
  2
• Both sellers picks quantities
• Then prices are called out until buyers
  quantity picked
• Sellers can pick new quantities if they want
• Then prices are called out until buyers
  quantity picked
• continue until a seller is not willing to
  respond (change quantity)
• Then sales are made at price that clears

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Oligopoly, Game Theory, and Competitive Strategy

• Outline
• Introduction
• Elements of Game Theory and the Concept of
  Equilibrium
• Applications of Simultaneous Move Games to Firm
  Strategy Quantity v. Price Competition
• Mixed Strategies
• Sequential Move Games
• Leadership
• Applications of Game Theory and Competitive
  Strategy

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A. Introduction

• Firms in perfect competition, monopoly, and
  monopolistic competition do not worry about the
  reactions of other firms in the industry.
• For the competitive and monopolistically
  competitive firms, this is because any firm has a
  small share of the market.
• For the monopoly there are no firms which produce
  a similar product.
• For many industries this independence among firms
  does not exist.
• Decisions by one firm will affect other firms
  producing like or similar products.
• These industries, characterized by a few firms,
  are generally referred to as oligopolies.

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Interdependence among Firms

• Because this interdependence between firms we can
  expect to observe that oligopolistic firms will
• Base any actions they make including
• pricing
• output
• research
• advertising and marketing
• on what they believe the response of other firms
  will be.
• They have an incentive to cooperate or collude.

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Example The Demand for GM Automobiles

• Demand for a product (GM automobile) depends on
  price of substitutes (Ford, Chrysler)
• Success of price changes depends on response of
  other firms

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PGM
DPFord high
DPFord low
QGM
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Mathematical game theory

• Mathematical game theory was developed to analyze
  situations when the benefits players (firms)
  receive depends on the actions of other players.
• We shall use some of the concepts of mathematical
  game theory to explore the strategies of firms in
  oligopolistic markets.
• In particular, we shall find that mathematical
  game theory will lead to predictions about
• firms competing in prices v. quantity
• when collusive agreements are likely to exist
• why firms differentiating products and
• strategies to deter entry.

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An Example of Oligopolistic Behavior The
Robinson-Chamberlain Model

• Suppose that in the industry (automobile) that
  firms do not want to lose market share. Then
• If a firm cut volume (to raise price) it will do
  it alone -- other firms will not follow.
• If a firm increases volume (lowering price) other
  firms will follow to avoid losing market share.
• Then if the firm increases volume it will not
  gain market share as all the other will follow.
• It keeps same market share and picks up sales
  according to market share.
• Price drops significantly since all firms
  increase volume,
• If it cuts volume it will lose share and price
  does not increase since other firms will not
  respond by cutting back volume.

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• Let the initial price of the GM automobile be P
  and the initial output be Q. Given the
  assumptions discussed above
• What does the demand curve look like if GM
  increases its price above the competitors (who do
  not increase their prices) -- how steep or flat
  is it?
• What does the demand curve look like if GM
  decreases its price (and so do the competitors)
  -- how steep or flat is it?
• What does the marginal revenue curve look like?

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The Kinked Demand Curve
D
MC
MR
15

• Model implies
• Price Rigidity in Oligopolies
• Consistent with notion that market share is a
  firm objective
• Not entirely consistent with profit maximization

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Game Theory and Firm Strategy

• Mathematical game theory, as applied to firm
  strategy, motivates the following conclusions
  about firm strategies and market outcomes
• 1) Show the interdependence of firms
• 2) Elasticity of demand is also related to the
  number of competitors.
• 3) Non-cooperative strategy can yield profits,
  but less than in monopoly.

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• 4) In a single period game that firms would want
  to compete in Q not P because of higher p..
• 5) Show that if firms do compete in price it is
  to their advantage to differentiate products.
• 6) A collusive agreement with price competition
  is price leadership, in which a dominant firm
  sets price and others follow.
• 7) If we consider competition over time, price
  marginal cost with price competition if firms
  make it clear that they will punish cheaters on
  the agreement.
• 8) Leadership is only effective if firm is
  committed to the policy and/or has the ability to
  retaliate.

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B. Elements of Game Theory and the Concept of
Equilibrium

• 1. Structure of a Game
• 1) Players
• 2) Strategies available to players (actions that
  can be taken)
• 3) Payoffs earned by players that depend on the
  choices of every player
• For a game to exist this information is necessary
  even if only available in a probabilistic sense
  (i.e., you don't know for certain what the payoff
  is).

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Simultaneous Move Games

• Game between Kroger's and Meijers.
• Each Wednesday they put out circulars advertising
  their specials.
• Suppose that they have the option of offering
  specials on deli or meats products.

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• The figure above is referred to as a payoff
  matrix.
• It denotes the payoffs (profit, benefit, revenue)
  for each combination of strategies.
• The 1st number in each cell is the payoff to
  Meijers and the 2nd is the payoff to Kroger's.
• For example, if both choose to feature Meat items
  the payoff is 50 to Meijers and 25 to Kroger's.

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• Dominant Strategy -- A strategy is said to be
  dominant if it always results in the highest
  payoff to a player regardless of the strategies
  of other players.
• What strategy should Kroger's choose?
• Does it depend on Meijer's strategy?
• Does it have a dominant strategy?
• What about Meijer?
• Does its strategy depend on Kroger's strategy?
• Does it have a dominant strategy?

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Other Examples
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Prisoners Dilemna
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• Rule 1 If you have a dominant strategy, use it.
  

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Dominated Strategies

• Dominated Strategy -- A strategy is said to be
  dominated if there exists some other strategy
  that always has a higher payoff (or equal payoff)
  regardless of the strategies of opponents.
• Consider a slightly different setting for
  competition between Kroger's and Meijer
• In this game we consider adding another strategy,
  running specials on bakery items.
• Payoffs for the other strategies have also
  changed.
• How will the bakery option affect the decisions
  of Kroger's and Meijer?

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• Rule 2 Eliminate all dominated strategies.

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Equilibrium and Choice of Strategies

• Consider Game 1

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• It is clear what Kroger's should do -- run the
  deli since it is a dominant strategy.
• But what should Meijer do?
• The answer is also clear, if Meijer understands
  Kroger's payoffs. Clearly Kroger will run the
  Deli special, so it only makes sense for Meijer
  to run the meat special.
• This is the Nash equilibrium -- what do we mean
  by equilibrium formally?
• The equilibrium or anticipated strategies are
  those strategies for which for every player,
  given the choice of strategies of the other
  players, can not increase his payoff.

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• What is the equilibrium in Game 5?

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• Rule 3 After eliminating dominated strategies
  and not having dominant strategies, choose as
  your strategy the equilibrium strategy.

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C. Applications of Simultaneous Move Games to
Firm Strategy Quantity v. Price Competition

• Cournot Equilibrium
• Model 2 firms (1 2) Homogenous Product
  Constant Marginal Cost
• Firm Strategy Choose output to maximize p
  believing that the other firm does not change its
  Q if you change yours.
• Results
• 1) Firm has downward sloping demand.
• 2) Price MC in equilibrium
• 3) Price
• 4) Firm's demand curve becomes more elastic as
  the of firms increases.
• 5) Price decreases as of firms increases.

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• Query
• Will equilibrium be at Price MC 1?
• Will output be 20, with 10 produced by each
  firms?

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D1
MR1
Q210
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Q2 6.67
Q1 6.67
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Reaction Function

• The reaction function for a player (firm) is the
  best (profit-maximizing) response (output) given
  the action (output) of the other player (firm)
• In this example we have
• Q1 10 - Q2/2
• Q2 10 - Q1/2
• How do we get this?
• Inverse Demand Curve is P21-Q1 Q2
• MC 1
• Firm 1s profit is PQ1 - MC1Q1
• (21-Q1-Q2)Q1 - Q1 21Q1 - Q12 - Q1Q2 - Q1
• Then profit-maximization implies
• d?1/dQ1 21 -2Q1 - Q2 - 1 0 or Q1 10 - Q2/2

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Cournot
1s Reaction
Equilibrium
2s Reaction
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Price (Bertrand) Competition

• Suppose that firms compete (set) prices not
  quantity -- does it make a difference?
• What does competing in prices mean?
• Set a price and sell to all willing to buy at
  that price

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Price Competition (continued)

• Consider price competition as a game where you
  can set above or below your opponent.
• Consider for a P MC

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• Whats equilibrium?
• P MC for both firms.

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Lesson

• Avoid price competition. If products are
  homogenous, then set production and sales if
  possible.

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P
RP
RP-?
D
P-?
Q
Q/2
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Differentiated Products

• Can not set quantity -- you meet all demand
• Hhow can you reduce the competitiveness of price
  competition?
• Product Differentiate
• create some monopoly power.
• Key product differentiation means that small
  changes in prices will not lead to capturing
  entire market and tremendous gains in profits.
• If quantity competition is not possible,
  differentiate your product to avoid direct price
  competition.

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Leadership

• Are there advantages to being a leader?
• When and how can a firm maintain a leadership
  position?
• In this section we examine two forms of
  leadership and show how it is advantageous to be
  a leader.
• In the next section we discuss how a leadership
  position can be maintained.
• In particular, to be a leader the firm must
• Be able to credibly commit to a strategy
• Know competitors' responses
• Punish competitors if they don't follow.

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Quantity Leadership

• Is there an advantage in committing to production
  and sales goals first?
• Stackelburg model Same as Cournot except 1 firm
  sets Q before the other firm.
• Result The firm that moves 1st will have higher
  p and output. This is because the other firm
  knows that your Q cannot change and will cut his
  to keep price up.

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Cournot vs. Stackelburg
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Price Leadership and the Dominant Firm

• Suppose instead a firm can set price (a dominant
  firm) and lets other firms sell as much as they
  want.
• This is a form of collusion, since it is agreed
  that firms won't undercut.
• How does the dominant firm decide what price to
  set?
• Based on his residual demand - the demand for
  his product given how much the smaller firms can
  supply

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Pricing with a Dominant Firm
P
DD
MRD
Q
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The Eightfold Path to Credibility
1.       Establish and use a reputation. 2.      
Write contracts 3.       Cut off
communication. 4.       Burn bridges behind
you. 5.       Leave the outcome to
chance. 6.       Move in small steps. 7.      
Develop Credibility through Teamwork. 8.      
Employ Mandated Negotiating Agents
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Commitment

• 3 major types of commitment
• Unequivocal move
• Retaliation with continued retaliation depending
  on competitor's moves.
• No action
• The 1st commitment can deter retaliation
• the 2nd can deter threatening moves
• the 3rd creates trust.

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Market Signals

• Prior Announcements of moves
• Reasons for prior annoucements preempting the
  competition (Stackelburg 1st mover, must be
  credible)
• threat (retaliation in a repeated game, again
  must be credible)
• tests of competitor sentiment (how will
  competition respond?)
• communicating pleasure or displeasure with
  competitors
• minimizing provocation

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Communicating Commitment

• Commitment is more credible if
• firm has assets to retaliate or move (excess cash
  reserves, excess productive capacity)
• history of past adherence to commitments
• long term contracts
• ability to detect compliance

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Competitive Moves

• Porter identifies 3 types of moves
• Cooperative Or Nonthreatening
• Threatening
• Key questions
• how likely is retaliation?
• how soon will retaliation come?
• how effective will retaliation be?
• how tough will retaliation be?
• can retaliation be influenced?
• Defensive Moves
• Most effective defense is to prevent a battle
  altogether. This means that firm must commit to
  a credible retaliation.

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Entry Deterence Monopolization

• How can firms maintain monopoly power?
• Key is to create barriers to entry
• How can this be done what strategies have been
  used?
• What about the legality of proceedings?

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Legal Cases

• We can learn about some of the strategies (mostly
  illegal) by examining cases
• U.S. v. Aluminum Company of American (1945)
• Strategy Excess Capacity
• Telex v. IBM (1975)
• Strategies Predatory pricing, Product design
• FTC v. Xerox (1975)
• Leasing bundling
• Patent Acquisition
• FTC v. Kellogg (1981)
• Brand Proliferation

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U.S. v. Alcoa (1945)

• Issue 1 What is the market?
• If include secondary ingots (scrap aluminum) 33
• Primary ingots, 90 (no other American producers
• This is what Judge Learned Hand chose
• Issue 2 Did it act to create monopoly or
  monopoly thrust upon it?
• The argument for having monopoly thrust upon it
• Market domination originated from patents
• Continued because of
• Economies of scale in conversion of bauxite to
  aluminum oxide
• Vertical integration
• Moderate pricing policy

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U.S. v. Alcoa, continued

• Issue 3 Does it matter how the monopoly arises
  or how it behaves?
• From Judge Hands decision
• It was an excuse, that Alcoa had not abused
  its power, it lay upon Alcoa to prove it had
  not. But the whole issue is irrelevant anyway
• The Act (Sherman Antitrust, 1914) had wider
  purposesMany people believe that possession of
  unchallenged economic power deadens initiative,
  discourages thrigt and depresses energy that
  immunity from competition is a narcotic and
  rivalry is a stimulant to industrial progess
• Congress did not condone good trusts and
  condemn bad trusts it forbade all.

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U.S. v. Alcoa, 3

• Issue 4 But did Alcoa actively attempt to
  monopolize and how?
• From Hands opinion
• not a pound of ingot has been produced by
  anyone else in the United States This
  continued control did not fall undesigned into
  Alcoas lap obviously it could not have done so.
• It was not inevitable that is should always
  anticipate increases in the demand for ingot and
  be prepared to supply them. Nothing compelled it
  to keep doubling and redoubling its capacity
  before others entered the field.
• Strategy Excess Capacity as a deterent

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Telex v. IBM (1975)

• Facts
• IBM dominated the rental market for mainframe
  CPUs for period 1964-1972
• Also sold complete systems CPU and periphals
  (terminals, tapes, card readers) along with
  Burroughs and Honeywell
• Smaller firms (Telex) produced only peripheral
  equipment
• These smaller firms made significant inroads into
  IBM peripheral equipment (plug compatible)
  changed much lower prices

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Telex v. IBM (1975), 2

• Facts
• IBMs responses
• Cut price of peripheral equipment competing with
  Telex
• Redesigned equipment to make (artificially) more
  difficulty to use Telex
• Lease agreements with reduced prices
• Large price reductions in peripheral equipment
  large price increases in CPUs

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Telex v. IBM (1975), 3

• The District Courts decision
• Ruled in favor of IBM
• As to pricing, the trial court found it was used
  by IBM only to a limited extent, that is, within
  the reasonable range. The resulting prices were
  reasonable in that they yielded reasonable
  profits.
• The record shows, during the period under
  consideration, that the parties and others in the
  market produced more advanced products better
  suited to the needs of the customers at lower
  prices

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Telex v. IBM (1975), 4

• Strategies by IBM
• Predatory pricing?
• Unnecessary product design to reduce compatibility

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FTC v. Xerox

• Facts
• In 1973 Xerox had 86 of copier industry 95 of
  plain paper.
• Xerox used a lease only policy
• Package leasing plans quantity discounts
• FTC claimed unfairly discriminated against
  customers
• All service done by Xerox
• Xerox had 1,700 patents numerous
  cross-licensing agreements

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FTC v. Xerox, 2

• FTC claimed
• Lease only policy unfairly discriminated against
  customers
• Reduced competition in supplies and services
• Patent policy allowed access to other firms
  patents
• Cross-licensing restricted competition

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FTC v. Xerox, 3

• Consent Decree signed by FTC Xerox
• No royalty on several of patents it was to
  license
• To refrain from acquiring patent licenses
• To eliminate pricing plans based on quantity
  leasing or purchasing plans
• To offer copiers for sale as well as lease

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FTC v. Xerox, 4

• Strategies by Xerox
• Leasing bundling to control all aspects of
  copier market (machines, repair, supplies)
• Control of market by patent acquisition
  cross-licensing

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FTC v. Kellogg (1981)

• Facts
• Kellogg, General Mills, General Foods had 80
  of market but no one firm controlled more than
  45
• FTC charged
• Firms had tacitly colluded cooperated to
  maintain exercise monopoly power
• They did this by
• Avoid price competition
• Focus on raising barriers to entry
• Excessive advertising
• Brand proliferation
• Control of shelf space

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FTC v. Kellogg (1981), 2

• FTC Evidence
• Extremely high profits in RTE cereal
• Lack of entry for decades
• Case was dismissed
• Our concept of a free competitive system does
  not envision imposition by government of
  permissible levels of advertising
• Brand proliferation is nothing more than the
  introduction of new brands which is a legitimate
  means of competition Respondents engage in
  intense, unrestrained and uncoordinated
  competition in the introduction of new products.

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Sequential Move Games

• Now we consider sequential move games where both
  players respond to each other's moves
  sequentially.
• We represent the sequential aspects of the game
  using a decision tree.
• Consider the following examples

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Centipede Game
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IBM versus Telex
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• How do we find a solution?
• Rule 4 Look ahead and reason back.

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A Repeated Game in Prices (Supergame)

• The Bertrand equilibrium (price competition) with
  its competitive result might seem a bit
  dissatisfying--two firms giving a competitive
  result.
• Suppose the game could be played
  repeatedly--would our results change?
• For example, suppose two firms start with
  agreeing to the monopoly price and a firm
  considers cheating this month by cutting its
  price a small amount.
• Will it want to do so if it believes that next
  period its competitor will cut his price to c and
  ruin all profits?

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Finite Game
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Infinite Horizon Games

• The outcomes change when we consider games with
  infinite horizons.
• Suppose that both firms have the following
  strategy charge the monopoly price, pm, in
  period 0 and charge pm in period t if in every
  period preceding t its competitor charged pm
  otherwise it sets its price at marginal cost, c,
  forever.
• This strategy is referred to as a trigger
  strategy because a single deviation triggers a
  halt in cooperation.
• Is a collusive agreement possible?

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Finite Game

• Game is 10 periods
• Demand is P 21 - Q1-Q2
• MC 1
• Monopoly P11, Profit100

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Finite Game

• Strategy
• Start with PM
• Do PM if competitor did PM
• Do P3 if competitor does P3
• Will this yield PM for entire game?
• Answer No -- last period both will cheat.

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2 Possible Strategies

• Punitive (Trigger)
• Set high price in period 1
• Keep price high in succeeding period if opponent
  has high price as well
• If opponent has low price, set low prices for
  forever after
• Tit for tat
• Set high price in period 1
• Price in each succeeding period imitates previous
  price of opponent

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Mixed Strategies

• Consider the game of Matching Pennies
• What is the equilibrium strategies?
• There is none in pure strategies
• Adopt a random strategy. 1 plays Heads (H) p of
  time 2 plays H q of time.
• But what strategy?

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• Player 1 should choose the probability of playing
  H (p) to maximize payoff given 2s strategy (q)
• ?1 p(3q (1-q)(-1)) (1-p)(-4q (1-q)4)
  -5p 12pq - 8q 3
• Then ??1/?p -5 12q 0 ? q 5/12
• 1s choice gives 2s strategy
• At q 5/12 the expected payoff from 1 doing H
  T are identical.

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• For 2 we have
• ?2 q(-p (1-p)) (1-q)(3p (1-p)(-2))
• -7pq 3q 5p - 2.
• ??2/?q 3 - 7p 0 ? p 3/7.