9781118041581

Table 10.2 depicts the percentage increase in market share of firm 1 (the row

player). For instance, if both firms adopt their first strategies, firm 1 loses (and

firm 2 gains) two share points. As described, the market share competition is

a zero-sum game. The competitors’ interests are strictly opposed; one side’s

gain is the other side’s loss. This being the case, it is customary to list only the

row player’s payoffs. The row player seeks to maximize its payoff, while the col-

umn player seeks to keep this payoff to a minimum. By doing so, firm 2 maxi-

mizes its own increase in market share.

In the advertising competition, there is a single equilibrium pair of strate-

gies: R2 versus C2. The resulting payoff (two here) is called the equilibrium out-

come.To check that this is an equilibrium, consider in turn each firm’s options.

Against C2, the best firm 1 can do is use R2. Switching to R1 or R3 means suf-

fering a loss of market share. Similarly, the best firm 2 can do against R2 is use

C2. If it switches to C1 or C3, it grants firm 1 a greater share increase, imply-

ing a greater loss in market share for itself. Thus, the strategies R2 and C2 are

profit maximizing against each other and constitute a Nash equilibrium.

To check that this is the only equilibrium, let’s identify each firm’s best

response (i.e., its most profitable action) to any action taken by its competitor.

Firm 1’s best response to C1 is R3, to C2 is R2, and to C3 is R1. Certainly, if

firm 1 could anticipate firm 2’s action, it would use its best response against it.

In Table 10.2, the payoffs from firm 1’s best responses to firm 2’s possible

actions are circled. The circles offer visual proof of the fact that firm 1 has no

dominant strategy. (Why? If a strategy were dominant, all the circles would line

up along the same row.) The table also identifies firm 2’s best responses: Its

best response to R1 is C1, to R2 is C2, and to R3 is C3. The resulting payoffs are

enclosed in squares. (Firm 2 has no dominant strategy.) The circles and squares

make it easy to identify the equilibrium outcome and strategies. A payoff is an

equilibrium outcome if and only if it is enclosed by botha circle and a square;

that is, it must be a best-response strategy for both players. Thus, we confirm

that 2 is the unique equilibrium outcome; R2 versus C2 are the equilibrium

strategies that generate this outcome.

The best a smart player can expect to get in a zero-sum game against an

equally smart player is his or her equilibrium outcome. If either side deviates

406 Chapter 10 Game Theory and Competitive Strategy

TABLE 10.2

Competitive Advertising

in a Mature Market

In this zero-sum game,

the firms’ equilibrium

strategies are R2

and C2.

Firm 2

C1 C2 C3

R1  2  14

Firm 1 R2 5 2 3

R3 7  3  5

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