(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 523

498 PART • Market Structure and Competitive Strategy as in many others, mixed strategies provide another solution, but not a very realistic one Hence, for the remainder of this chapter we will focus on pure strategies 13.4 Repeated Games • repeated game Game in which actions are taken and payoffs received over and over again We saw in Chapter 12 that in oligopolistic markets, firms often find themselves in a prisoners’ dilemma when making output or pricing decisions Can firms find a way out of this dilemma, so that oligopolistic coordination and cooperation (whether explicit or implicit) could prevail? To answer this question, we must recognize that the prisoners’ dilemma, as we have described it so far, is limited: Although some prisoners may have only one opportunity in life to confess or not, most firms set output and price over and over again In real life, firms play repeated games: Actions are taken and payoffs received over and over again In repeated games, strategies can become more complex For example, with each repetition of the prisoners’ dilemma, each firm can develop a reputation about its own behavior and can study the behavior of its competitors How does repetition change the likely outcome of the game? Suppose you are Firm in the prisoners’ dilemma illustrated by the payoff matrix in Table 13.8 If you and your competitor both charge a high price, you will both make a higher profit than if you both charged a low price However, you are afraid to charge a high price because if your competitor charges a low price, you will lose money and, to add insult to injury, your competitor will get rich But suppose this game is repeated over and over again—for example, you and your competitor simultaneously announce your prices on the first day of every month Should you then play the game differently, perhaps changing your price over time in response to your competitor’s behavior? In an interesting study, Robert Axelrod asked game theorists to come up with the best strategy they could think of to play this game in a repeated manner (A possible strategy might be: “I’ll start off with a high price, then lower my price But then if my competitor lowers his price, I’ll raise mine for a while before lowering it again, etc.”) Then, in a computer simulation, Axelrod played these strategies off against one another to see which worked best TIT-FOR-TAT STRATEGY As you would expect, any given strategy would work better against some strategies than it would against others The objective, however, was to find the strategy that was most robust—that would TABLE 13.8 PRICING PROBLEM Firm Firm Low price High price Low price 10, 10 100, ؊50 High price ؊50, 100 50, 50 See Robert Axelrod, The Evolution of Cooperation (New York: Basic Books, 1984)