Oligopoly and Game Theory Notes

Oligopoly

  • Definition: A market structure with only a few suppliers of a good or service.

    • Typically involves two, three, or four sellers.

    • Products have no close substitutes.

    • Significant barriers to entry prevent new firms from entering the market if economic profits exist.

    • Possibility of collusion exists among firms.

Sources of Oligopoly

  1. Natural Oligopoly: Occurs when market demand is met at the lowest cost with only a few firms.

    • Example: A natural duopoly exists when two firms can each produce 30 units to meet market demand at the lowest cost. A natural oligopoly with three firms exists when each produces 20 units.

  2. Ownership: Control of a significant portion of a resource.

  3. Legal: Government regulations or patents limit the number of firms.

  • A legal oligopoly can exist even when market demand and firm costs could support more firms.

  • Barriers to entry are essential for the existence of an oligopoly.

Interdependence and Cooperation

  • Interdependence: Each firm's profit is significantly affected by the actions of other firms in the oligopoly.

  • Cooperation: Firms may have an incentive to cooperate due to their interdependence.

    • Firms can form a cartel: An agreement to limit output, raise prices, and increase profits.

    • Cartels are illegal in the United States.

  • Incentives: A small number of firms creates the opportunity for cooperation, while interdependence creates the incentive.

Problems with Oligopoly

  • If firms cooperate, they can behave like a monopoly, which leads to:

    • Restricted output

    • Higher prices

    • Economic profit

Game Theory

  • Definition: A tool for studying strategic behavior in situations where the outcome of one's choices depends on the choices of others.

  • Allows modeling of expected behaviors of actors with mutual recognition of interdependence.

  • Four Common Features of All Games:

    • Rules: The setting, actions players can take, and consequences.

    • Strategies: All possible actions each player can take.

    • Payoffs: The possible outcomes for each player, given each strategy.

    • Outcome: The ultimate result of the game.

The Prisoner's Dilemma

  • A classic example in game theory demonstrating the difficulty of cooperation even when it is mutually beneficial.

  • Rules:

    • Two prisoners are caught committing a minor crime but are suspected of a more serious crime.

    • They are held separately and cannot communicate.

    • Each is told that the other is confessing to the more serious crime.

    • If neither confesses, each gets a 2-year sentence for the minor crime.

    • If both confess, each gets a 5-year sentence for both crimes.

    • If only one confesses, he gets a 1-year sentence for cooperating, while the other gets a 10-year sentence.

  • Strategies:

    • Each prisoner has two options: confess or deny the more serious crime.

  • Possible Outcomes:

    • Both confess

    • Both deny

    • A confesses, B denies

    • B confesses, A denies

  • Payoff Matrix: Represents the years of prison each prisoner faces in each scenario.

    Prisoner B Confess

    Prisoner B Deny

    Prisoner A Confess

    5, 5

    1, 10

    Prisoner A Deny

    10, 1

    2, 2

  • The Dilemma:

    • Both prisoners would be better off if they both denied the crime.

    • However, each knows that if the other denies, it's in their best interest to confess.

    • Assuming the other will confess, the best choice for the first prisoner is also to confess.

  • Outcome:

    • Each player is rational and acts in their own best interest.

    • Best Outcome: Both deny (2 years each).

    • Equilibrium Outcome: Both confess (5 years each).

    • This is a Nash equilibrium: each individual's best strategy, given the strategy of the other player.

  • The Game Changes Over Time:

    • Incentives evolve as the game progresses.

Oligopoly Price-Fixing Game

  • A game similar to the prisoner's dilemma that occurs in a duopoly. *Natural Duopoly:

    • Two firms can mee the market demand at the least cost.

Collusion

  • Two firms enter a collusive agreement to restrict output, raise the price, and increase profits.

  • By colluding, firms can act like a monopolist and share economic profits.

  • Firms in a collusive agreement operate as a cartel.

  • Cartels are illegal in the United States.

  • Strategies firms in a cartel can pursue:

    • Honor the agreement

    • Break the agreement

  • Possible combinations of action:

    • Both firms honor the agreement

    • Both firms break the agreement

    • One firm honors and the other breaks

    • The other firm breaks, and the first one honors

No Collusion

  • Each firm produces 3m units at a price of 12.

  • There are no economic profits (ATC = price).

${}Cartel Agreement Enables Economic Profits$

  • Each firm agrees to reduce production to 2m units.

  • The price rises from 12 to 22.

  • Economic profit = 6m.
    *Firms Collude to Act like a Monopoly
    *ATC increases from 12 to 19

Incentive

  • Firms in cartels have incentive to cheat

  • When each firm produces 2m units, the price (22) > MC (8).

  • If one firm increased its output back to 3m, they could make a large economic profit.

  • The total quantity is now 5m.

  • The price is now 18.

Break Agreement

  • Firms have incentive to break the agreement

  • Economic Profit = 18m,

  • Economic Loss=2m

  • The firm that breaks the agreement: economic profit increases to 18m

  • The firm that honors the agreement: now a 2m economic loss

Eventually

  • Eventually, Both Firms Break Agreement.

  • Both firms increase their output to 3m units.

  • The price falls back to 12.

  • There are no economic profits.
    *Firms Have Incentive to Break Agreement

Firm B Break

Firm B Honor

Firm A Break

0, 0

+18m, -3m

Firm A Honor

-3m, +18m

+3m, +3m

  • The Game Changes Over Time

  • The incentive change as the game is played

Equilibrium

  • Both Firms Break Collusive Agreement

  • The quantity & price are the same as the competitive market, and firms make zero economic profit.

  • Nash Equilibrium

  • Cartels in Oligopoly are Unstable

Solutions

  • One solution for two firms in oligopoly is for the two firms to merge, or for one firm to buy the other firm.

  • This eliminates the need for an agreement, that eventually fails, to restrict output and raise prices.

  • In the United States, antitrust laws would prohibit these types of merger.

Oligopoly Summary

  1. Few Sellers

  2. Unique Product

  3. Barriers to Entry/Exit

  • Oligopoly: 2 or 3 firms meet market demand at lowest ATC

  • Firms few: so they are interdependent and may cooperate

  • Oligopoly can be a problem: if firms cooperate they can act like one monopoly (by restricting output, charging higher prices and make an Economic Profit in the long run).

  • Game theory helps us understand strategic actions of interdependent players.

  • Oligopoly firms can form a cartel and agree to collude.

  • Cartels, Collusion, Agreements by sellers are illegal in the United States

  • Cartels are unstable. Firms have an incentive to break agreements.