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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.
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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.
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. 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)
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. 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)
