Oligopoly, Collusion and Antitrust

1
Oligopoly, Collusion and Antitrust

2
Game Theory

• An analytic approach that is concerned with the
  behavior of independent decision-makers whose
  fortunes are linked in an interplay of collusion,
  conflict and compromise
• Begins with a set of decision makers or players
• There is a set of strategies available to each
  player

3
Game Theory some definitions and assumptions

• Outcomes for each player depend on the actions of
  all players
• Referred to as the pattern of payoffs
• Protocol of play describes the rules of the game
  (i.e., move order, information conditions and
  knowledge that each player has at every stage)

4
Game Theory some definitions and assumptions

• Players are assumed to be rational with well
  defined goals
• Modelers Objective - use the rules of the game
  to determine equilibrium

5
Game Theory some definitions and assumptions

• Equilibrium a strategy profile consisting of a
  best strategy for each of the players of the
  game
• Equilibrium strategies are the strategies players
  pick in trying to maximize their individual
  payoffs

6
Game theory is concerned with the following
question

• If I believe my competitors are rational and act
  to maximize their own profits, how do I take
  their behavior into account when making my own
  profit-maximizing or utility maximizing decisions
• Question can be difficult to answer even when
  conditions are completely symmetric

7
The Advertising Game

• Consider a duopoly in which firms dont compete
  on price
• p15 and Q100
• Unit cost5 so profit10
• The firms do compete via advertising
• Firms can compete at a low rate at a cost of 100
  or at a high rate at a cost of 200
• Assume advertising does not affect demand but it
  does affect market share
• If both firms advertise in equal amounts they
  will split the market otherwise 75 share to the
  high advertiser

8
The Advertising Game

• We can calculate the payoffs from each rate
  (15-5)50-100 400 if both are low (15-5)25-100
  if one is low and the other high .
• Construct the payoff matrix which shows the
  payoffs to both players (firm 1, firm 2)
• Suppose each firm chooses a strategy
  simultaneously choose hw much to advertise

9
The Advertising Game
10
The Advertising Game

• If Firm 2 choose to high advertising then high
  advertising is optimal for Firm 1
• If Firm 2 choose to low advertising then high
  advertising is optimal for Firm 1
• For Firm 1 high advertising is dominant
• If Firm 1 choose to high advertising then high
  advertising is optimal for Firm 2
• If Firm 1 choose to low advertising then high
  advertising is optimal for Firm 2
• For Firm2 high advertising is dominant

11
What is the Advertising Game?
12
Would it matter if one of the players went first?
13
No first mover advantage

• If firm 1 went first and
• advertises low, firm 2 will advertise high
• If firm 1 advertises high, firm 2 will advertise
  high
• What if B goes first

14
Some more terms.

• Dominant strategy is a players best strategy
  irrespective of what the others do
• Easy to deduce what happens in games with
  dominant strategies
• A situation in which each player is choosing the
  best strategy available to him given the
  strategies chosen by others is called Nash
  Equilibrium
• Dominant strategy equilibrium is a special case
  of Nash

15
Consider the next payoff matrix
16
Does A have a dominant Strategy

• If B chooses b-1, a-2 is optimal
• If B chooses b-2, a-1 is optimal
• A doesnt have a dominant strategy Its optimal
  strategy depends on what B does
• If A chooses a-1, b-1 is optimal
• If B chooses a-2, b-1 is optimal
• For B, b-1 is dominant

17
What should A do?

• Put itself in Bs shoes. What decision is best
  from Bs perspective
• A2,b1 is a Nash Equilibrium
• Firm As optimal decision depends on what Firm B
  does

18
Alternative Rules

• Expected value rule a-1,b-1 but a-1 is not an
  optimal response to b-1
• Maximin for A is a 1, maximin for B is b 1,
  again not Nash

19
Nash Equilibrium

• Each player is doing the best it can do given the
  actions of its opponents.
• If the player has no incentive to deviate the
  strategies are stable

20
Comparison of dominant strategy and Nash
equilibrium

• Dominant strategy equilibrium Im doing the
  best I can no matter what you do Your doing the
  best you can no matter what I do
• Nash equilibrium Im doing the best I can do
  given what you are doing Your doing the best you
  can given what I am doing

21
Compatibility Game

• Firm 1 is a supplier of videocassette recorders
• Firm 2 is a supplier of videocassettes
• Firm 1s cost of producing VHS VCR is slightly
  less than that of producing Beta
• Firm 2s cost of producing Beta cassettes is
  slightly less
• These firms are the sole exporters to a country
  that has no production capabilities for either
  product
• Consumers are indifferent between the products

22
The Compatibility Game
23
What should firms do in this setting

• If Firm 2 chooses beta, beta is optimal for Firm
  1
• If Firm 2 chooses vhs, vhs is optimal for Firm1
• If Firm 1 chooses beta, beta is optimal Firm 2
• If Firm 1 chooses VHS, VHS is optimal Firm 2
• Both firms using Beta is a Nash equilibrium
• Both Firms using VHS is a Nash equilibrium
• Without more information we have no way of
  knowing which equilibrium will result

24
Oligopoly

• Essence of oligopoly is recognized
  interdependence
• Number of firms is so few that firms have to
  worry about what other firms are doing and will
  do.
• Many theories of oligopoly behavior but Cournot
  is still the most widely used.

25
Cournot

• A monopolist can achieve the same profit
  maximizing outcome by choosing the most
  profitable price or the most profitable quantity.
• With oligopoly it makes a difference whether
  firms engage in price or output competition

26
Quantity Competition

• Consider a duopoly facing a linear market demand
  curve
• Goods produced are homogeneous
• Outputs are chosen simultaneously
• Price is determined by
• P100 Q
• P100 (q1q2)
• Assume MC 0

27
Collusive Solution

• Assume two firms decide to work together as a
  monopolist
• Max profit MRMC0
• MR 100 2Q 0
• 100 2 Q
• Q50
• Implies P 50
• Profit PQ50502500
• Collusive solution if firms split the profit -
  1250

28
Competitive Solution

• MCP0
• Here the supply curve is the horizontal axis
• P100-Q implies Q100
• Profit will be 0

29
Cournot Solution

• Each firm is aware that increasing output will
  reduce t he market price P
• In making its own output decision, each firm
  assumes its competitors output is fixed each
  chooses the highest payoff given the decision of
  the other

30
Cournot

• What is the rationale?
• For any output q2 there is a profit maximizing q1
• Firm 1 acts as a monopolist over the remaining
  demand
• Plot firm 1s optimal q as a function of q2 and a
  corresponding one for firm 2

31
Reaction Curves
q2
Intersection defines Cournot equilibrium which
is also Nash
rc2
rc1
q1
32
Reaction Curves

• Firm 1s producing q1
• Demand for Firm 2
• P (100-q1) q2
• Since q1 is regarded as a constant
• MR (100-q1) 2q2
• RC2 can be found by setting MC2MR2

33
Reaction Curves

• Firm 2s Demand
• q2 50 q1/2
• Analogously, firm 1s Demand is
• q1 50 q2/2
• Rearranging terms and by substitution
• -2q2 100 50 q2/2
• -2q2 1/2 q2 -50
• -3/2q2 -50 implies q233 1/3
• q1 50 33 1/3 ½ 33 1/3

34
Alternative Story Stackleberg Model

• Here Firm 1 sets q1 first then firm2 sets q2
• look at last decision first
• How do we find optimal q2 given q1
• Reaction Function
• P 100 (50-q1/2)-q1
• P 50 - q1/2
• MR 50 q1 implies q1 50
• q2 50 q1/2 implies q2 25

35
Alternative Story Stackleberg Model

• P 100 q2 - q1 100 25 50 25
• Q 75
• Firm 1 profit 25 50 1250
• Firm 2 profit 25 25 625