Chapter 10

Game theory and strategic behavior

Game Theory

• Game theory was pioneered by the mathematician John Von Neumann and the economist Oskar Morgensten in 1944.

• It is an instrument used to analyze cooperation and conflicts between firms in oligopolistic markets.

• In general, game theory is concerned with the choice of the best or optimal strategy in conflict situations.

Example

• Game theory can help a firm determine the conditions under which lowering its price would not trigger a ruinous price war.

• Game theory would help us understand why cheating leads to the collapse of a cartel.

The features of a game

• Every game theory model includes:

- The players

- Strategies

- The payoffs

The players

• There are the decision-makers.

The strategies

• These are the actions available to each player

Payoff

• The payoff is the outcome or consequence of each action

• We distinguish between a zero-sum games and a nonzero-sum games

A Zero-sum games

• It is one in which the gain of one player comes at the expense and is exactly equal to the loss of the other player.

• Example: If firm A increases its market share by 10% and firm B loses 10% of its market share.

A nonzero sum game

• It is one in which the gains of one player do not come at the expense of the other player.

• Example: If firm A and Firm B increase their profits as a result of one action.

Dominant Strategy

• The dominant strategy is the optimal choice for a player no matter what the other player does.

Payoff matrix for an advertising game

Firm B

Advertise Don’t advertise

Firm A

Advertise (4, 3) (5, 1)

Don’t advertise

(2, 5) (3, 2)

The Nash equilibrium

• Not all games have a dominant strategy for each player.

• It is the situation in where each player chooses his or her optimal strategy, given the strategy chosen by the other player.

Payoff matrix for the advertising game

Firm B

advertise don’t

advertise

Firm A

don’t

(4, 3) (5, 1)

(2, 5) (6, 2)

The prisoner’s Dilemma

Confess

Don’t confess

Confess don’t confess

(5, 5) (0, 10)

(10, 0) (1,1)

Individual B

Individual A

Price competition and the prisoner’s dilemma

Low price High price

Low price

High price

(2, 2) (5, 1)

(1, 5) (3, 3)Firm A

Firm B

In-class problems

• Problem #5 page 426

• Problem #8 page 426