1. Oligopolies & Game Theory
Econ 201
Oligopolies & Game Theory

2. Figure 12.4 Duopoly Equilibrium in a Centralized Cartel

3. Duopoly What are the strategic options and the payoffs? Form a cartel
Forego additional profits from increasing output beyond assigned quota
Cheat on the Cartel
Increase production unilaterally (output effect)
If only you increase output, price doesn’t fall too much (price effect)
Compete on price
Final equilibrium moves towards competitive market price
No monopoly rents (or + economic profits)

4. Game Theory
Game theory is a methodology that can be used to analyze both cooperative and non-cooperative oligopolies.
Recognizes the interdependence of the firms’ actions
Using a payoff matrix to describe options (strategies) and payoffs
Firms are profit maximizers!

5. Figure 12.7 Xbox and PlayStation 2 Payoff Matrix for Advertising

6. Nash Equilibrium Nash equilibrium
a solution to a non-cooperative game involving two or more players
each player is assumed to know the equilibrium strategies of the other players
no player has anything to gain by changing only his own strategy unilaterally
Hence, a Nash equilibrium will be stable (once you get there!)

7. Determining the Dominate Strategy (Single Nash)
A dominant strategy occurs when one strategy is best for a player regardless of the rival’s actions. (rival’s actions don’t matter)
Dominate strategy equilibrium—neither player has reason to change their actions because they are pursuing the strategy that is optimal under all circumstances.
Here the dominant strategy is for each firm to advertise (it is also a Nash Equilibrium)

8. Multiple Equilibria
Sometimes there are come cases where there are multiple Nash equilibria.
In this case, the outcome is uncertain.
Firms will have an incentive to collude.
An example:
Sony/Microsoft can add one of two new features
One feature appeals only to YOUTH market
Other feature appeals only to TEEN market
Incentive to reach agreement on both firms offering the same new (one only) feature

9. Payoff Table Multiple Nash Equilibria

10. Prisoner's Dilemma
A prisoner’s dilemma occurs when the dominate strategy leads all players to an undesired outcome.

11. Figure 12.9 Prisoners’ Dilemma

12. Best Outcome Neither confesses
But without collusion/agreement – how do you guarantee this outcome?
Enforcement issues (price, output, quotas)
Law & Order
Why we keep suspects separated!
Prevent collusive agreements

13. An Economic Application of Game Theory: the Kinked-Demand Curve
Above the kink, demand is relatively elastic because all other firm’s prices remain unchanged. Below the kink, demand is relatively inelastic because all other firms will introduce a similar price cut, eventually leading to a price war. Therefore, the best option for the oligopolist is to produce at point E which is the equilibrium point

14. Game Theory: Kinked Demand Curve and Nash Equilibrium
Firm B
(Competitor)
Raise Price
Don’t Change
Lower Price
(-5%)
(-1%->+5%)
(-2%->+1%)
(A) -5%
(A)-5%
(B) -5%
(B) +5%
(B)+1%
Firm A
(You)
+5%
(A)-1%
(B) 0
(A) +1%
(A)+1%
(A) -2%
(B) -1%
(B) -2%

15. Nash Equilibrium
If firm facing kinked demand curve tries to raise price:
Other firms do not
As demand is highly elastic and other firms are “close” substitutes
Loses market share and revenues
If firm lowers price
Competitors match price decreases

16. Nash Equilibrium
If firm facing kinked demand curve tries to raise price:
Other firms do not
As demand is highly elastic and other firms are “close” substitutes
Loses market share and revenues
If firm lowers price
Competitors match price decreases

17. Features of a Nash Equilibrium
In a non-cooperative oligopoly, each firm has little incentive to change price.
This represents a Nash Equilibrium, where each firm’s pricing strategy remains constant given the pricing strategy of the other firms.
Firms have no incentive to change their strategy.

18. Non-Cooperative Cartels
Either
Some degree of price competition
Firms engage in highly competitive pricing
Similar outcome as perfect competition
Firms have some market power
Resembles monopolistic competition
Bilateral monopoly with price competition
or Stable prices prevail
Non-collusive
Firms choose not to compete because of kinked demand curve

19. Non-cooperative Oligopolies
Competitive/psuedo-competitive behavior (non-cooperative)
Perfect Competition (almost): firms undercut each other’s prices
competition between sellers is fierce, with relatively low prices and high production
Outcome may be similar to PC or Monopolistic Competition
Nash equilibrium
Firms avoid “ruinous” price competition by keeping prices stable and avoiding price competition (undercutting each others prices)
May lead to product proliferation and/or extensive advertising (non-price competition)

20. Figure 12.3 U.S. 2003 Advertising-to-Sales Ratio for Selected Products and Industries

21. Game Theory Models of Oligoploy
Stackelberg's duopoly. In this model the firms move sequentially (see Stackelberg competition).
Cournot's duopoly. In this model the firms simultaneously choose quantities (see Cournot competition).
Bertrand's oligopoly. In this model the firms simultaneously choose prices (see Bertrand competition).
Monopolistic competition. A market structure in which several or many sellers each produce similar, but slightly differentiated products. Each producer can set its price and quantity without affecting the marketplace as a whole.