Oligopoly

1
Oligopoly
2
Oligopoly - Competition among the Few

• In an oligopoly there are very few sellers of the
  good.
• The product may be differentiated among the
  sellers (e.g. automobiles) or homogeneous (e.g.
  gasoline).
• Entry is often limited either by legal
  restrictions (e.g. banking in most of the world)
  or by a very large minimum efficient scale (e.g.
  overnight mail service) or by strategic behavior.
• Sill assuming complete and full information.

3
How Oligopolists Compete

• In an oligopoly
• firms know that there are only a few large
  competitors
• competitors take account of the effects of their
  actions on the overall market.
• To predict the outcome of such a market,
  economists must model the interaction between
  firms and so often use game theory or game
  theoretic principles.

4
Three Basic Models

• Competition in quantities Cournot-Nash
  equilibrium
• Competition in prices Bertrand-Nash equilibrium
• Collusive oligopoly Chamberlin notion of
  conscious parallelism
• It is very useful to know some basic game theory
  to understand these models as well as other
  oligopoly models.

5
Game Theory Setup

• List of players all the players are specified in
  advance.
• List of actions all the actions each player can
  take.
• Rules of play who moves and when.
• Information structure who knows what and when.
• Payoffs the amount each player gets for every
  possible combination of the the players actions.

6
A Classic Two Player, Two Action Game - The
Prisoners Dilemma
Chris
Lie
Confess
Lie
-1, -1
-6, 0
Roger
Confess
0, -6
-5,-5

• Rogers best response function
• If Chris lies, then Roger should confess (check
  out left column, 1st entries)
• If Chris confesses, then Roger should confess
  (right column, 1st entries)
• Confess is a dominant strategy for Roger
• Chriss best response function
• If Roger lies, then Chris should confess (see top
  row, 2nd entries)
• If Roger confesses, then Chris should confess
  (bottom row, 2nd entries)
• Confess is a dominant strategy for Chris

7
A Classic Two Player, Two Action Game - The
Prisoners Dilemma
Chris
Lie
Confess
Lie
-1,-1
-6, 0
Roger
Confess
0, -6
-5,-5

• There is a single dominant strategy equilibrium
• Rogers confesses and
• Chris confesses
• They both go to jail for 5 years
• Note the game is played simultaneously and
  non-cooperatively!
• Ways to sustain the cooperative equilibrium (lie,
  lie)
• different payoff structures
• repeated play and trigger strategies

8
Question Will There Always Be A Dominant
Strategy Equilibrium?

• AnswerNO!
• Then what?
• Look for Nash Equilibrium.

9
Nash Equilibrium

• Named after John Nash - a Nobel Prize winner in
  Economics.
• The Nash Non-cooperative Equilibrium of a game is
  a set of actions for all players that, when
  played simultaneously, have the property that no
  player can improve his payoff by playing a
  different action, given the actions the others
  are playing.
• Each player maximizes his or her payoff under the
  assumption that all other players will do
  likewise.

10
Another Example - The Price Game
Chris
Low
High
Low
20, 20
60, 0
Roger
High
0, 60
100, 100

• Rogers best response function
• If Chris goes low, then Roger should go low
  (check out left column, 1st entries)
• If Chris goes high, then Roger should high (right
  column, 1st entries)
• There is no dominant strategy for Roger
• Chriss best response function
• If Roger goes low, then Chris should go low (see
  top row, 2nd entries)
• If Roger goes high, then Chris should go high
  (bottom row, 2nd entries)
• There is no dominant strategy for Chris

11
Another Example - The Price Game
Chris
Low
High
Low
20, 20
60, 0
Roger
High
0, 60
100, 100

• Rogers best response function
• If Chris goes low, then Roger should go low
• If Chris goes high, then Roger should high
• Chriss best response function
• If Roger goes low, then Chris should go low
• If Roger goes high, then Chris should go high
• Two Nash Equilibria (low, low) and (high, high)
• Respective Nash equilibrium payoffs (20,20) and
  (100,100)
• Which equilibrium will prevail? Good question.

12
Another Example - The Simultaneous Entry Game
Roger - the entrant
enter
not enter
Chris - the incumbent
fight
fight
accommodate
accommodate
(Roger 0,Chris 0)
(Roger 2, Chris 2)
(Roger 1,Chris 5)
(Roger 1,Chris 5)

• Get two Nash equilibria
• (enter, accommodate) and (not enter, fight)

13
Another Example - The Sequential Entry Game
Roger - the entrant
enter
not enter
Chris - the incumbent
fight
fight
accommodate
accommodate
(Roger 0,Chris 0)
(Roger 2, Chris 2)
(Roger 1,Chris 5)
(Roger 1,Chris 5)

• Still get two Nash equilibria
• (enter, accommodate) and (not enter, fight)
• Only one, however, is credible (enter,
  accommodate)

14
Another Two Player, Two Action Example

• The game has two players 1 2.
• Player 1 can move up or down (actions).
• Player 2 can move left or right (actions).
• If player 1 moves up and player 2 moves left
  then player 1 gets 1 and player 2 gets 0
  (payoffs).
• The table shows all possible action pairs and
  their associated payoffs.

15
Player 1s Best Strategies

• If player 2 plays right, the best strategy
  (action) for player 1 is to play up.
• In this case player 1 will get a payoff of 1,
  underlined.

16
Player 2s Best Strategies

• If player 1 plays up then player 2s best
  strategy (action) is to play right.
• In this case, player 2 gets a payoff of 2,
  underlined.

17
Nash Equilibrium

• The table shows the best strategy (actions) for
  player 1 against both of player 2s possible
  actions (underlined first numbers).
• The table also shows the best strategy (actions)
  for player 2 against both of player 1s possible
  actions (underlined second numbers).
• Notice that both numbers are underlined in the
  cell up,right. This is the Nash Equilibrium.
• If player 1 plays up the best thing for player
  2 to do is play right and vice versa.

18
A Non-cooperative Outcome (Cournot-Nash Duopoly -
Competition in Quantities)

• Developed by Antoine Augustin Cournot in 1838.
• In a two firm oligopoly (called a duopoly), if
  both firms set their output levels assuming that
  the other firms strategic choice variable
  (quantities in Cournot competition) is fixed, the
  equilibrium outcome is a Cournot Nash
  Non-cooperative Equilibrium. (Note Cournot
  solved this oligopoly model many years before
  Nash invented the equilibrium definition we are
  using here).

19
Setup of the Duopoly Problem Monopoly Outcome

• The table at the right shows the monopolists
  best choice for the simple market demand curve
  shown, assuming only whole quantities can be
  chosen.
• The monopolist maximizes profits at X3, P14,
  with economic profits of 21.
• Assuming only whole quantities can be produced,
  the competitive equilibrium is X6, P8, the
  last price at which economic profits are not
  negative (FC0 and MC7 for all X).

20
Duopoly Game Competition in Quantities

• Suppose that there are two firms X and Y with
  identical total cost curves that are the same
  ones shown for the monopolist in the previous
  slide total cost7Xi
• The payoff matrix above shows the economic
  profits of Firm X (left entry) and Firm Y (right
  entry) for each possible quantity supplied of 0
  to 4 units.
• The payoff for a firm is determined by finding
  the price that prevails for the total quantity
  supplied (Firm X Firm Y), then multiplying each
  quantity by this price and subtracting the firms
  total costs for that quantity.
• Note demand price is PD20-2X where XXX XY
• Example Firm X supplies 3 and Firm Y supplies 1
  - so X4 and P12
• Firm Xs payoff (3 x 12) - 21 15
• Firm Ys payoff (1 x 12) - 7 5

21
Duopoly Game Nash Equilibrium in Quantities

• The boxes marked in yellow are the best moves for
  Firm X given the indicated quantity supplied by
  Firm Y.
• The boxes marked in green are the best moves for
  Firm Y given the indicated quantity supplied by
  Firm X.
• The payoff for the cell (X supplies 2, Y supplies
  2) is (10, 10). This cell is the Nash
  Non-cooperative Equilibrium for this game because
  it represents the best move for Firm X given that
  Firm Y chooses its best move and the best move
  for Firm Y given that Firm X chooses its best
  move.
• Duopoly outcome Total quantity supplied 2 2
  4. Market price 12. Total economic profits
  10 10 20.
• Monopoly outcome Total quantity supplied 3.
  Market price 14. Total economic profits 21.
• Competitive outcome Total quantity supplied 6.
  Market price 8. Total economic profits 6.

22
Properties of the Cournot-Nash Equilibrium for
Duopoly

• When the duopolists compete in quantities, we can
  compare the outcome to both the monopoly and
  competitive outcomes.
• Each duopolist produces less than a monopolist in
  the same market but together they produce more
  than the monopolist and less than the amount two
  competitive firms would have produced with the
  same cost structure and demand curves.
• The sum of the economic profits of each duopolist
  is less than the economic profits of a monopoly
  in the same market.
• The market price is less than the one a
  monopolist would charge but more than the
  competitive price.
• Deadweight loss is less than for a monopoly in
  the same market but still positive, thus greater
  than the deadweight loss from a competitive
  market.

23
Duopoly Game Competition in Prices (J. Bertrand
1883)

• Firm X and Y have the same cost structure and
  face the same market as in the previous example.
• Now, instead of playing a game in quantities,
  they play a game in prices allowing only the
  choices indicated.
• The payoff matrix above shows the economic
  profits of Firm X (left entry) and Firm Y (right
  entry) for each possible price chosen 8, 10,
  12, 14, 16.
• If the two firms choose the same price they split
  the market in half otherwise, the firm that
  chooses the lower price sells the market quantity
  and the other firm sells nothing.
• Example Firm X charges 12 and Firm Y charges
  12
• Market X 4, both firms sell 2 units at 12 and
  have total costs of 14.
• Firm X payoff Firm Y payoff 2 x 12 - 14
  10.
• Example Firm X charges 10 and Firm Y charges
  8.
• Market X 6, Firm Y sells all 6 units, Firm X
  sells nothing.
• Firm X payoff 0 Firm Y payoff 6 x 8 - 42
  6.

24
Duopoly Game Bertrand-Nash Equilibrium in Prices

• The boxes marked in yellow are the best moves for
  Firm X given the indicated quantity supplied by
  Firm Y.
• The boxes marked in green are the best moves for
  Firm Y given the indicated quantity supplied by
  Firm X.
• The payoff for the cell (X charges 8, Y charges
  8) is (3, 3) and the payoff for the cell (X
  charges 10, Y charges 10) is (7.5, 7.5). Both
  cells are the Nash Non-cooperative Equilibria for
  this game.
• Duopoly competition in prices in this market does
  not have a unique equilibrium (a common
  occurrence in game theory).
• This game predicts that the market price
  fluctuates between 8 and 10.
• This game predicts that the market quantity
  fluctuates between 4 and 6.
• It is not uncommon for the competition in
  quantities game to give different results from
  the competition in prices game.

25
Performance Bertrand vs. Cournot

• When the duopolists compete in prices, we can
  compare the outcome to both the monopoly and
  competitive outcomes, but it can be more
  difficult to find an equilibrium.
• Classic results (when an equilibrium exists and
  is unique).
• N1 then XBN XSM and PBN PSM
• Ngt1 then XBN X and PBN P
• Bertrand compared to Cournot.
• N1 then XCN XSM and PCN PSM
• Ngt1 then X gt XCN gt XSM and Plt PCN lt PSM
• N gets large enough, XCN X and PCNP
• Results have different implications for
  anti-trust action.
• Should MCI be able to merge with Sprint? N goes
  from 3 to 2.
• Should Coke be allowed to merge with Dr. Pepper?
  Should Pepsi be allowed to merge with 7-Up?
• Good questions.

26
A Cooperative Outcome (Collusion)

• The duopolists can do better than the Nash
  Non-cooperative Equilibrium.
• Because the equilibrium is non-cooperative, we
  have ruled out the possibility of collusion
  between the two firms.
• Collusion means that the firms explicitly
  cooperate in choosing a market price and the
  division of output between them.
• If the duopolists collude and divide up the
  market privately, they can produce the monopoly
  quantity and divide the monopoly economic
  profits.
• Since the monopoly economic profits are more than
  the sum of the duopoly profits, the duopolists
  are better off if they collude.
• When we allow the possibility of collusion the
  game can turn out differently.

27
Duopoly Game Collusion

• In our previous example Firm X and Firm Y can
  cooperate and agree to charge 14 and to produce
  3 units between them.
• They will earn the monopoly profits of 21 in
  this case.
• There is 1 of additional profit compared to the
  quantity game and at least 6 of additional
  profit compared to the price game.
• Any division of this extra profit between the two
  firms makes both firms willing to collude rather
  than play the non-cooperative game.
• The possibility of collusion is excluded from the
  non-cooperative games by the assumption that the
  firms strategies consist of either choosing a
  quantity or choosing a price.
• Collusion involves choosing a market quantity (or
  price), production quotas for each member and a
  division of the monopoly profit between the two
  firms.

28
Collusion Problems

• Frequently, side payments are essential to the
  cooperative solution. Especially when the cartel
  members have different cost structures.
• OPEC example Iran and Saudi Arabia.
• Irans marginal costs increase more quickly than
  do Saudi Arabias.
• Suppose they do not cooperate and end up at the
  Cournot-Nash solution Get profits such that
  ?SA ?I ?joint
• Suppose they cooperate and implement the monopoly
  solution Get profits such that ?SA ?I
  ?joint
• Since Iran has the crummy marginal cost curve, it
  will be told not to produce very much in the
  collusive arrangement.
• Could be that ?SA gt ?SA and ?joint gt ?joint
  but ?I gt ?I !
• If joint cartel profit is larger than the joint
  non-cooperative profit, then there is enough to
  make side payments to Iran to get Irans
  cooperation.
• Will the side payments be made? Are they legal?
  Good questions.

29
Collusion Problems

• Side payments aside, there is also a compelling
  incentive to cheat on the cartel arrangement.
• Cheating often means that someone is violating
  the cartels production limits - producing more
  than they agreed to.
• More ends up on the market than was supposed to.
• The price ends up lower than it was supposed to.
• The cartel starts to experience dissention.
• Steps are taken to shore up the cartel agreement.
• This strong internal tendency to cheat led Milton
  Friedman to once opine that cartels were nothing
  more than a flash in the pan.
• How successful are cartels? How often do they
  form? Are they able to substantially raise the
  market? For how long?
• Good questions.