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Analyzing Payoff Tables 405

move, CBS should place its hit at 9 P.M. as a best response. The network out-

comes are audiences of 39 million and 28 million viewers, respectively.

In this variation on the basic example, CBS’s optimal action requires a sim-

ple kind of reflexivethinking: putting itself in NBC’s shoes. Notice that the pre-

dicted outcome has the property that each player’s strategy is a best response

against the chosen strategy of the other. Thus, neither network could improve

its profit by second-guessing the other and moving to a different strategy.

CHECK

STATION 1

Consider the following competition between two department stores, each of which must

decide what kind of clothing to promote. Does either store have a dominant strategy?

What is the predicted outcome?

Store 2

Promote Promote

Girls’ Clothes Women’s Clothes

Promote

Girls’ Clothes 0, 0 4, 2

Store 1 Promote

Children’s Clothes 2, 2 2, 4

Equilibrium Strategies

What action should a decision maker take to achieve his objectives when com-

peting with or against another individual acting in her own interests? The prin-

cipal answer supplied by game theory is as follows:

In settings where competitors choose actions independently of one another (and

so cannot collude), each player should use an equilibrium strategy, one that max-

imizes each player’s expected payoff against the strategy chosen by the other. This

is known as a Nash equilibrium.

In both versions of the ratings battle example, the predicted outcome satisfies this

definition; that is, it is an equilibrium. The following example illustrates a com-

petitive setting in which neitherside has a dominant strategy. Nonetheless, each

side has an equilibrium strategy, and that is how each should play.

MARKET-SHARE COMPETITION Consider two duopolists who compete

fiercely for shares of a market that is of constantsize. (The market is mature

with few growth opportunities.) Each firm can adopt one of three marketing

strategies in an attempt to win customers from the other. The payoff table in

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