1. Game Theory and Oligopoly
Game theory is a useful tool for understanding the interactions of a group of sellers that is small enough so that they take account of each other’s possible reactions to their own decisions about how much to provide at what price.

2. A Demand Schedule for Water
Suppose the marginal cost is zero.
What would the price be under monopoly?
Under perfect competition?
With two sellers in the market?
See next slide
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3. Price and Quantity Supplied Under Monopoly and Perfect Competition
The price of water in a perfectly competitive market would be driven to where the marginal cost is zero:
P = MC = $0
Q = 120 gallons
The price and quantity in a monopoly market would be where total profit is maximized:
P = $60
Q = 60 gallons
How much will each of two sellers provide and what price will each charge?

4. Jack and Jill Oligopoly Game
Jack’s Decision
Sell 40 Gallons
Sell 30 Gallons
Jack gets
$1,600 profit
Jill gets
Jill gets
$2,000 profit
Jack gets
$1,500 profit
Sell 40
Gallons
Jill’s
Decision
Jill gets
$1,500 profit
Jack gets
$2,000 profit
Jill gets
$1,800 profit
Jack gets
Sell 30
Gallons
The Monopoly Optimum
Copyright©2003 Southwestern/Thomson Learning

5. Will Jack and Jill Get to the Monopoly Optimum?
The prisoners’ dilemma provides insight into the difficulty in maintaining cooperation.
Often people (firms) fail to cooperate with one another even when cooperation would make them better off.

6. The Prisoners’ Dilemma
The prisoners’ dilemma is a “game” between two people awaiting trial for a crime they have committed, but for which the DA has insufficient evidence to convict. It illustrates why cooperation is difficult to maintain even when it is mutually beneficial.
The dominant strategy is the best strategy for a player to follow regardless of the strategies chosen by the other players.
A dominant strategy will not always exist.

7. The Prisoners’ Dilemma
Dominant
strategy
Bonnie’ s Decision
Confess
Remain Silent
Bonnie gets 8 years
Clyde gets 8 years
Bonnie gets 20 years
Clyde goes free
Confess
Clyde’s
Decision
Bonnie goes free
Clyde gets 20 years
gets 1 year
Bonnie
Clyde gets 1 year
Remain
Silent
Cooperative solution
Copyright©2003 Southwestern/Thomson Learning

8. Jack and Jill Oligopoly Game
Dominant Strategy
Jack’s Decision
Sell 40 Gallons
Sell 30 Gallons
Jack gets
$1,600 profit
Jill gets
Jill gets
$2,000 profit
Jack gets
$1,500 profit
Sell 40
Gallons
Jill’s
Decision
Jill gets
$1,500 profit
Jack gets
$2,000 profit
Jill gets
$1,800 profit
Jack gets
Sell 30
Gallons
Cooperative solution
= Monopoly Optimum
Copyright©2003 Southwestern/Thomson Learning

9. The Nuances of Self Interest
Self interest in isolation (the dominant strategy) is different from self interest in a cooperative context. But both a dominant strategy and a cooperative strategy reflect the self interest of the players. No question here of altruism, duty, obligation, or any other motive than the hedonistic utility of the players.

10. Another Concept of Equilibrium for an Oligopoly
A Nash Equilibrium is a situation in which interacting economic agents each choose their best strategy given the strategies that all the others have chosen. And these strategies are mutually compatible.

11. Jack and Jill Oligopoly Game
Jack’s Decision
Sell 40 Gallons
Sell 30 Gallons
Jack gets
$1,600 profit
Jill gets
Jill gets
$2,000 profit
Jack gets
$1,500 profit
Sell 40
Gallons
Jill’s
Decision
Jill gets
$1,500 profit
Jack gets
$2,000 profit
Jill gets
$1,800 profit
Jack gets
Sell 30
Gallons
Copyright©2003 Southwestern/Thomson Learning

12. Jack and Jill Oligopoly Game
Nash Equilibrium
Jack’s Decision
Sell 40 Gallons
Sell 30 Gallons
Jack gets
$1,600 profit
Jill gets
Jill gets
$2,000 profit
Jack gets
$1,500 profit
Sell 40
Gallons
Jill’s
Decision
Jill gets
$1,500 profit
Jack gets
$2,000 profit
Jill gets
$1,800 profit
Jack gets
Sell 30
Gallons
Copyright©2003 Southwestern/Thomson Learning