Oligopoly

1
Oligopoly

• A market structure in which there are few firms,
  each of which is large relative to the total
  industry.
• Key idea Decision of firms are interdependent.

2
The Simple Mathematics of Oligopoly

• Given P 200 2Q
• TC 500 40Q 2Q2
• What is the profit maximizing price? 160
• If this firms current price was 150 and it
  raised its price, how would its competition
  respond?
• IF YOU DO NOT KNOW THE COMPETITORS RESPONSE, IT
  IS DIFFICULT TO PREDICT WHAT THE NEW DEMAND CURVE
  WILL BE!!! THEREFORE OUR SIMPLE PROBLEM HAS
  BECOME A BIT MORE COMPLICATED!!

3
Game Theory

• Game Theory the study of how individuals make
  decisions when they are aware that their actions
  affect each other and when each individual takes
  this into account.
• History Introduced in 1944 by John von Neumann
  and Oskar Morgenstern in The Theory of Games and
  Economic Behavior.
• The work of von Neuman and Morgenstern was
  expanded upon by John Nash.

4
Introduction to Game Theory

• A game is a situation in which a decision-maker
  must take into account the actions of other
  decision-makers. Interdependency between
  decision-makers is the essence of a game.
• In games people must make strategic decisions.
  Strategic decisions are decision that have
  implications for other people.
• Strategy a decision rule that describes that
  actions a player will take at each decision
  point.
• Normal form game a representation of a game
  indicating the players, their possible
  strategies, and the payoffs from alternative
  strategies.

5
Cooperative and Non-Cooperative Games

• Non-Cooperative Games are games in which players
  cannot enter binding agreements with each other
  before the play of the game.
• Cooperative Games are games in which players can
  enter binding agreements with each other before
  the play of the game.
• In class we only review non-cooperative games.

6
Two Types of Games

• Simultaneous move game Game in which each
  player makes decisions without knowledge of the
  other players decision.
• Examples Pitching in baseball, Calling plays in
  football
• Sequential move game Game in which one player
  makes a move after observing the other players
  move.
• Example Chess

7
Elements of a Game

• Set of Players.
• Order of Play.
• Description of the information available to any
  player at any point during the game.
• Set of actions available to each player when
  making a decision.
• Outcomes that result from every possible
  sequence of actions by the players.
• A payoff from the outcomes.
• Strategic situations with the above elements is
  considered to be well defined.

8
Actions, Strategies, and Payoffs

• Actions The set of choices available at each
  decision in a game.
• Pure strategy a rule that tells the player what
  action to take at each of her information sets in
  the game.
• Mixed strategy when players can choose randomly
  between the actions available to them at every
  information set.
• Example Play calling in sports is a mixed
  strategy.
• Payoffs, for our purposes, consist of either
  profits to firms, or income to individuals.
  Payoffs can also be characterized in terms of
  utility.

9
Solving Games Nash Equilibrium

• Solution Concept a methodology for predicting
  player behavior.
• Nash Equilibrium - a collection of strategies one
  for each player, such that every player's
  strategy is optimal given that the other players
  use their equilibrium strategy.
• The Opie Equilibrium Inside Business 10-1

10
Dominant and Dominated Strategies

• Payoff matrix a matrix that displays the
  payoffs to each player for every possible
  combination of strategies the players could
  choose.
• Dominant Strategy a strategy that is always
  strictly better than every other strategy for
  that player regardless of the strategies chosen
  by the other players.
• Dominated Strategy a strategy that is always
  strictly worse than some other strategy for that
  player regardless of the strategies chosen by the
  other players.

11
Weakly Dominate Strategies

• Weakly dominant strategy - a strategy that is
  always equal to or better than every other
  strategy for that player regardless of the
  strategies chosen by the other players.
• Weakly Dominated Strategy a strategy that is
  always equal to or worse than some other strategy
  for that player regardless of the strategies
  chosen by the other players.

12
Prisoners Dilemma

• Scenario Two people are arrested for a crime
• The elements of the game
• The players Prisoner One, Prisoner Two
• The strategies Confess, Dont Confess
• The payoffs
• Are on the following slide
• Payoffs read Prisoner 1, Prisoner 2

13
Prisoners Dilemma, cont.

• Prisoner 2
• Confess Dont Confess
• Confess 6 years, 6 years 1 year, 10 years
• Prisoner 1
• Dont Confess 10 year, 1 year 3 years, 3 years
• Dominant strategy equilibrium In this game, the
  dominant strategy for each prisoner is to
  confess. So the outcome of the game is that they
  each get six years.
• This illustrates the prisoners dilemma games in
  which the equilibrium of the game is not the
  outcome the players would choose if they could
  perfectly cooperate.

14
The Advertising Game

• Scenario Two firms are determining how much to
  advertise.
• The elements of the game
• The players Firm 1, Firm 2
• The strategies
• High advertising, low advertising

15
Advertising Game, Cont.

• The payoffs are as follows (payoffs read 1,2)
• Firm 2
• High Low
• High 40,40 100, 10
• Firm 1
• Low 10, 100 60,60
• Dominant strategy equilibrium In this game, the
  dominant strategy for firm 1 and firm 2 is high.
  So the outcome of the game is 40,40.
• Again, this is an example of the prisoners
  dilemma. The equilibrium of the game is not the
  outcome the players would choose if they could
  cooperate.

16
More Prisoner Dilemmas

• Industrial Organization Examples
• Cruise Ship Lines and the move towards glorious
  excess. Royal Caribbean offers a cruise with an
  18 hole miniature golf course. Princess Cruises
  has a ship with three lounges, a wedding chapel,
  and a virtual reality theater.
• Owners of professional sports teams and the
  bidding on professional athletes.
• Non-IO Examples
• Politicians and spending on campaigns.
• Worker effort in teams. The incentive exists to
  shirk, a strategy that if followed by all
  workers, reduces the productivity of the team.
  More on shirking later.

17
Iterated Dominant Strategies

• What if a dominant strategy does not exist?
• We can still solve the game by iterating towards
  a solution.
• The solution is reached by eliminating all
  strategies that are strictly dominated.

18
Example of Iterated Dominance

• Down is Firm 1, Across is Firm 2

19
Alternative Solution Strategies

• Nash Equilibrium - a strategy combination in
  which no player has an incentive to change his
  strategy, holding constant the strategies of the
  other players.
• Joint Profit Maximization This is the objective
  of a cartel.
• Cut-Throat A strategy where one seeks to
  minimize the return to her/his opponent.
• Secure Strategy A strategy that guarantees the
  highest payoff given the worst possible scenario.
• How does the previous game change when we change
  the objectives of the players?
• This is one of the advantages of game theory. We
  do not have to assume profit maximization. We
  still need to be able to identify the objectives
  of the players.

20
Infinitely Repeated Games

• A game that is played over and over again forever
  in which players receive payoffs during each play
  of the game.

21
Present Value Across an Infinite Horizon

• If the profits earned by a firm are the same in
  each period and the horizon is infinite, the
  present value of a firm simplifies to the
  following formula
• PVFIRM PROFIT (1i)/(i)

22
Trigger Strategy

• A strategy that is contingent on the past play of
  a game and in which some particular past action
  triggers a different action by a player.
• Example Two firms charge high prices. Cheating
  is a trigger which forces the non-cheating firm
  to cut prices.

23
Should a firm cheat?

• A firm should cheat if the one-time payoff from
  cheating exceeds the present value of future
  profits earned from not cheating.
• Payoff from cheating vs.
• non-cheating profits (1i)/i
• Key issue
• Size of the payoff from cheating
• Interest rate earned

24
Pricing Game

• The payoffs are as follows (payoffs read 1,2)
• Firm 2
• Low High
• Low 0,0 200, 10
• Firm 1
• High 10, 200 20,20
• Dominant strategy equilibrium In this game, the
  dominant strategy for firm 1 and firm 2 is low.
  So the outcome of the game is 20,20.
• There is an incentive to cheat an earn an
  one-time payoff of 100.

25
Solving the Pricing Game

• Present value from cheating 200
• Present value from not cheating
• 20 (1i)/i
• At what interest rate is cheating not a good
  idea?
• 200 20(1i)/i
• 200i 20 20i
• 180i 20
• i 1/9 11.1
• If the interest rate is less 11.1, the payoff
  from cheating is too low.

26
Factors impacting collusion

• Knowing identity of rivals
• Knowing the customers of rivals
• Knowing when rivals cheat
• Be able to punish rivals who cheat

27
Firm and Industry characteristics that impact
collusion

• Number of firms
• More firms increase monitoring costs
• Size of firms
• Smaller firms cannot afford monitoring
• History of the markets
• Tacit collusion cannot work if punishing is
  ineffective.
• Punishment mechanisms
• Can the punishing firm price discriminate?
• Price discrimination lowers the cost of punishing.

28
Mixed Strategy

• Pure Strategy is a rule that tells the player
  what action to take at each information set in
  the game.
• Mixed strategy allows players to choose randomly
  between the actions available to the player at
  every information set. Thus a player consists of
  a probability distribution over the set of pure
  strategies.
• Examples of mixed strategy games
• Play calling in sports
• To shirk or not to shirk

29
The Shirking Game

• Scenario A worker is hired but does not wish to
  work. The firm will not pay the worker if there
  is no work, but the firm cannot directly observe
  the workers effort level or output.
• Players The worker, the firm
• Strategy Work or not work, monitor or not
  monitor
• Payoffs Work pays 100, but the workers
  reservation wage is 40.
• Worker can produce 200 in revenue, but it costs
  80 to monitor.

30
The Shirking Game, Cont.

• There is no dominant strategy, or iterated
  dominant strategy.
• There is also no clear Nash Equilibrium. In
  other words, no combination of actions makes both
  sides happy given what the other side has chosen.

31
The Shirking Game, cont.

• There are many mixed strategies. The worker could
  work with probability (p) of 0.7, 0.6. 0.25,
  etc... The same is true for the firm. Which
  mixed strategy should they choose?
• If the worker is most likely to shirk, the firm
  should monitor. Likewise, if the firm is more
  likely to monitor, the worker should work. In
  any scenario, no Nash equilibrium will be found.
  The key is to find a strategy that makes the
  opponent indifferent to his/her potential
  choices.
• A person is indifferent when the expected return
  from action A equals the expected return form
  action B.

32
The Firms Solution

• How much should the firm monitor?
• E(work) 60p 60(1-p) 60
• E(shirk) 0p 100(1-p) 100 - 100p
• 100 - 100p 60
• 40 100p
• p .40
• The worker is indifferent when the probability of
  monitoring is 40 and the probability of not
  monitoring is 60.

33
The Workers Solution

• How much should the worker work?
• E(monitor) 20p -80(1-p) 100p - 80
• E(Not monitor) 100p -100(1-p) 200p - 100
• 100p -80 200p - 100
• 20 100p
• p .2
• The firm is indifferent when the probability of
  working is 20 and the probability of not working
  is 80.
• How does the cost of monitoring and the workers
  reservation wage impact behavior?