(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 517
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492 PART 3 • Market Structure and Competitive Strategy
13.3 The Nash Equilibrium Revisited
In §12.2, we explain that
the Cournot equilibrium is
a Nash equilibrium in which
each firm correctly assumes
how much its competitor will
produce.
To determine the likely outcome of a game, we have been seeking “self-enforcing,” or “stable” strategies. Dominant strategies are stable, but in many games,
one or more players do not have a dominant strategy. We therefore need a more
general equilibrium concept. In Chapter 12, we introduced the concept of a Nash
equilibrium and saw that it is widely applicable and intuitively appealing.5
Recall that a Nash equilibrium is a set of strategies (or actions) such that each
player is doing the best it can given the actions of its opponents. Because each player
has no incentive to deviate from its Nash strategy, the strategies are stable. In the
example shown in Table 13.2, the Nash equilibrium is that both firms advertise:
Given the decision of its competitor, each firm is satisfied that it has made the
best decision possible, and so has no incentive to change its decision.
In Chapter 12, we used the Nash equilibrium to study output and pricing by
oligopolistic firms. In the Cournot model, for example, each firm sets its own
output while taking the outputs of its competitors as fixed. We saw that in a
Cournot equilibrium, no firm has an incentive to change its output unilaterally
because each firm is doing the best it can given the decisions of its competitors.
Thus a Cournot equilibrium is a Nash equilibrium.6 We also examined models in which firms choose price, taking the prices of their competitors as fixed.
Again, in the Nash equilibrium, each firm is earning the largest profit it can
given the prices of its competitors, and thus has no incentive to change its price.
It is helpful to compare the concept of a Nash equilibrium with that of an
equilibrium in dominant strategies:
Dominant Strategies:
Nash Equilibrium:
I’m doing the best I can no matter what you do.
You’re doing the best you can no matter what I do.
I’m doing the best I can given what you are doing.
You’re doing the best you can given what I am doing.
Note that a dominant strategy equilibrium is a special case of a Nash
equilibrium.
In the advertising game of Table 13.2, there is a single Nash equilibrium—both
firms advertise. In general, a game need not have a single Nash equilibrium.
Sometimes there is no Nash equilibrium, and sometimes there are several (i.e.,
several sets of strategies are stable and self-enforcing). A few more examples
will help to clarify this.
THE PRODUCT CHOICE PROBLEM Consider the following “product choice”
problem. Two breakfast cereal companies face a market in which two new variations of cereal can be successfully introduced—provided that each variation is
introduced by only one firm. There is a market for a new “crispy” cereal and a
5
Our discussion of the Nash equilibrium, and of game theory in general, is at an introductory level.
For a more in-depth discussion of game theory and its applications, see James W. Friedman, Game
Theory with Applications to Economics (New York: Oxford University Press, 1990); Drew Fudenberg
and Jean Tirole, Game Theory (Cambridge, MA: MIT Press, 1991); and Avinash Dixit, David Reiley, Jr.,
and Susan Skeath, Games of Strategy, 3rd ed. (New York: Norton, 2009).
6
A Stackelberg equilibrium is also a Nash equilibrium. In the Stackelberg model, however, the rules of
the game are different: One firm makes its output decision before its competitor does. Under these
rules, each firm is doing the best it can given the decision of its competitor.
