OLIGOPOLY AND GAME THEORY Phillip J Bryson Marriott School, BYU

Introduction n Game Theory pioneered at Princeton n John von Neumann (mathematician/physicist) and Oscar Morgenstern (Austrian economist) n Initial promise, later disappointment, and revival

The Payoff Matrix. n Shows outcomes resulting from different possible decisions n Probabilities can be attached to the outcomes.

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

Payoff matrices illustrated: Al’s n Outcomes: u five years each if both confess. u three years each if both consistently deny u one year for turning state’s evidence and convicting the other for 10 years. A Confess Not confess Confess510 B Not confess1 3 u Al’s dominant strategy is to confess!

Payoff matrices illustrated:Benito’s n Outcomes: u five years each if both confess. u three years each if both consistently deny u one year for turning state’s evidence and convicting the other for 10 years. A Confess Not confess Confess51 B Not confess10 3 u This is a mirror of Al’s payoff matrix. Benito’s dominant strategy is also to confess.

Game Outcomes n 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 n Nash Equilibrium. Each player chooses the best strategy given the other’s behavior, when there’s no dominant strategy. n 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 n 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 n 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. n 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 n 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 n Cooperation would have provided a better outcome, however, with both firms saving the advertising costs. u Note that with low expenditures being agreed upon, each would earn 100 units of profit. u With the higher expenditures, each firm received only 80 units of profit.