No Such Thing as a Free Lunch: Principles of Economics (Part 70)

“95% of economics is common sense”

― Ha-Joon Chang, Economics: The User's Guide: A Pelican Introduction

Monopolistic Competition and Oligopoly

(Part E)

by

Charles Lamson

Game Theory

The firms in Courno's model from last post do not anticipate the moves of the competition. Yet in choosing strategies in an oligopolistic market, real-world firms can and do try to guess what the opposition will do in response.

In 1944, John Von Neumann and Oskar Morgenstern published a path-breaking work in which they analyzed the set of problems, or games, in which two or more people or organizations pursue their own interests and in which no one of them can dictate the outcome. During the last few years, game theory has become an increasingly popular field of study and a fertile area for research. The notions of game theory have been applied to analyses of firm behavior, politics, international relations, and foreign policy. In 1994, the Nobel Prize in economic science was awarded jointly to 3 early game theorists: John F. Nash of Princeton, John C. Harsanyi of Berkeley, and Reinhard Seltan of the University of Bonn.

Game theory goes something like this: In all conflict situations, and thus all games, there are decision makers (or players), rules of the game, and payoffs (or prizes). Players choose strategies without knowing with certainty what strategy the opposition will use. At the same time, though, some information that indicates how their opposition may be "learning" may be available to the players.

Figure 6 illustrates what is called a payoff matrix for a very simple game. Each of two firms, A and B, must decide whether to mount an expensive advertising campaign. If each other does not, the firm that does will increase its profit by 50 percent (to $75,000), while driving the competition into the loss column. If both firms decide to advertise, they will each earn profits of $10,000. They may generate a bit more demand by advertising, but not enough to offset the expense of the advertising itself.

The result of the game in Figure 7 is an example of what is called a prisoner's dilemma. The term comes from a game in which two prisoners (call them Ginger and Rocky) are accused of robbing a local 7-Eleven together, but the evidence is shaky. If both confessed, they each get five years in prison for armed robbery. If each one refuses to confess, they get convicted of a lesser charge, shoplifting, and get 1 year in prison each. The problem is that the district attorney has offered each of them a deal independently. If Ginger confesses and Rocky does not, Ginger goes free and Rocky gets 7 years. If Rocky confesses and ginger does not, Rocky goes free and Ginger gets 7 years. The payoff matrix for the prisoner's dilemma is given in Figure 7.

By looking carefully at the payoffs you may notice that both Ginger and Rocky have dominant strategies: to confess. That is, Ginger is better off confessing regardless of what Rocky does, and Rocky is better off confessing regardless of what Ginger does. The likely outcome is thus that both will confess, even though they would be better off if they both kept their mouths shut.

There are many games in which one player does not have a dominant strategy but in which the outcome is predictable. Consider the game in Figure 8(a) in which C does not have a dominant strategy. If D plays the left strategy, C will play the top strategy. If D plays the right strategy, C will play the bottom strategy. What strategy will D choose to play? If C knows the options, she will see that D has a dominant strategy and is likely to play it. D does better playing the right-hand strategy regardless of what C does; he can guarantee himself a $100 win by choosing right and is guaranteed to win nothing by playing left. Because D's behavior is predictable (he will play the right hand strategy), C will play bottom. When all players are playing their best strategy given what their competitors are doing, the result is called a Nash equilibrium.

Now suppose that the game in Figure 8(a) were changed. Suppose that all the payoffs are the same except that if D chooses left and C chooses bottom, C loses $10,000 [Figure 8(b)]. While D still has a dominant strategy (playing right), C now stands to lose a great deal by choosing bottom on the off chance that D chooses left instead. When uncertainty and risk are introduced, the game changes. C is likely to play top and guarantee herself a $100 profit instead of playing bottom and risk losing $10,000 in the off chance that D plays left. A maximum strategy is one chosen by a player to maximize the minimum gain that it can earn. In essence, one who plays a maximum strategy assumes that the opposition will play the strategy that does the most damage. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 294-296*

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