492 PART • 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 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 You’re doing the best you can no matter what I 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 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) 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