OLIGOPOLY AND GAME THEORY

Phillip J Bryson

Marriott School, BYU

Introduction Game Theory pioneered at

Princeton John von Neumann

(mathematician/physicist) and Oscar Morgenstern (Austrian economist)

Initial promise, later disappointment, and revival

The Payoff Matrix.

Shows outcomes resulting from different possible decisions

Probabilities can be attached to the outcomes.

The Payoff Matrix.

Consider the Prisoner’s Dilemma. Al and Benito, partners in crime, may have to strategize against each other after they have been apprehended. Each has a payoff matrix.

Separated (so they can’t communicate), each must decide whether to confess.

Payoff matrices illustrated: Al’s

Outcomes: five years each if both confess. three years each if both consistently deny one year for turning state’s evidence and convicting the other for 10

years.

A

Confess Not confess

Confess 5 10

B Not confess 1 3

Al’s dominant strategy is to confess!

Payoff matrices illustrated:Benito’s

Outcomes: five years each if both confess. three years each if both consistently deny one year for turning state’s evidence and convicting the other for 10 years.

A

Confess Not confess

Confess 5 1

B Not confess 10 3

This is a mirror of Al’s payoff matrix. Benito’s dominant strategy is also to confess.

Game Outcomes

Dominant Strategy. This is the one superior to any alternative strategy, regardless of what the opponent does. If each player has a dominant strategy, the game has a dominant strategy equilibrium.

Game Outcomes Nash Equilibrium. Each player chooses the best strategy given the other’s behavior, when there’s no dominant strategy.

Note the excellent movie, “A Beautiful Mind,” which presents an entertaining version of the life of John Nash. Interestingly, in the movie, Nash seems to accommodate in such a way to the dilemma he is in that he reaches a Nash Equilibrium.

Game Outcomes

In the prisoner’s dilemma game here, the dominant strategy makes each player worse off. The prisoners could both have been better off if they had adopted a cooperative strategy. The ability to communicate about joint implications can be important in a one-shot game. Here, the dominant strategy must, unfortunately for A & B, be played out.

Payoff Matrix

Firm 1

Low expends High expends

Firm 2 Low expends 1=100 1=150

(2=100) (2=60)

High expends 1 =60 1=80

(2 = 150) (2=80)

Application: Excessive Advertising In oligopoly markets, the strategy game is repeated so firms have

the opportunity to learn from past experience. Here, however, we again play a one-shot prisoner’s dilemma game.

Assume Firms 1 and 2 competing for market share and profit, both hoping to expand sales by advertising.

Firm 1

Low expends High expends

Firm 2 Low expends 1=100 1=150

(2=100) (2=60)

High expends 1 =60 1=80

(2 = 150) (2=80)

Excessive Advertising: Outcomes In this non-cooperative game, achieving a dominant strategy

gives 80 units of profit for each competitor. Here, both have refused to lose the market to the opponent’s aggressive advertising instincts.

Firm 1

Low expends High expends

Firm 2 Low expends 1=100 1=150

(2=100) (2=60)

High expends 1 =60 1=80

(2 = 150) (2=80)

Excessive Advertising: Outcomes Cooperation would have provided a better outcome, however, with both firms saving the

advertising costs. Note that with low expenditures being agreed upon, each would earn 100 units of profit. With the higher expenditures, each firm received only 80 units of profit.