(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 523
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498 PART 3 • 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 1 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. 9 (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 2
Firm 1
9
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).
