[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

First
duopolist
Figure 12.10
Do not
collude
(Do not
restrict
output)
Collude
(restrict
output)
Do not collude
(Do not restrict
output)
$0.5 billion
$0.4 billion
Second duopolist
$0.5 billion
$1.3 billion
THE PROBLEM OF COLLUSION AS A
PRISONER’S DILEMMA
worse off, each serving three years. The prisoner’s dilemma is a
simple game in which both parties are made worse off by independently
following their own self-interest. Both would be better off if
they could get together to agree on a story, and to threaten the other
$0.4 billion if he deviated from the story.
The prisoner’s dilemma game can be used to illustrate the problem
of collusion among oligopolists. Let us work with the example of
a duopoly, which is a market with two firms. Figure 12.10 shows the
$1 billion
level of profits of each if both collude and restrict output (both get $1
billion), if neither restricts output (both get $0.5 billion), or if one
restricts output and the other does not (the one that does not gets
$1.3 billion, the one that does gets $0.4 billion). As each firm thinks
through the consequences of restricting output, it will quickly realize
that if the other firm restricts output, its best strategy is to expand
output; and if the other firm fails to restrict output, its best strategy
is also to expand output. Thus the firm finds that regardless of what
the other does, it pays to expand output rather than to restrict it.
Since the other firm will reach the same conclusion, both will conclude
that it does not pay to restrict output. Hence, both will expand
output; they do not collude to restrict output.
The central point is that even though the firms see that they could both be
Collude
(restrict output)
$1.3 billion
$1 billion
The payoffs for the duopolists delineate a prisoner’s
dilemma. Both firms would be better off if both colluded
(restricted output), but their individual incentives lead each
to not collude (not restrict output).
better off colluding, the individual incentive to cheat dictates the strategy that
each follows.
So far we have considered the prisoner’s dilemma when each player makes only
a single move to complete the game. But if firms interact over time, then they have
additional ways to try to enforce their agreement. For example, suppose each oligopolist
announces that it will refrain from cutting prices as long as its rival does.
But if the rival cheats on the collusive agreement, then the first oligopolist will
respond by increasing production and lowering prices. This strategy is called tit for
tat. If this threat is credible—as it may well be, especially after it has been carried
out a few times—the rival may decide that it is more profitable to cooperate and
keep production low than to cheat. In the real world, such simple strategies may
play an important role in ensuring that firms do not compete too vigorously in
markets that have only three or four dominant firms.
The commonness and success of such strategies have puzzled economists. The
logic of game theory suggests that these approaches would not be effective. Consider
what happens if the two firms expect to compete in the same market over the next
ten years, after which time a new product is expected to come along and shift the
entire configuration of the industry. It will pay each firm to cheat in the tenth year,
when there is no possibility of retaliation, because the industry will be completely
altered in the next year. Now consider what happens in the ninth year. Both firms can
figure out that it will not pay either one of them to cooperate in the tenth year. But
if they are not going to cooperate in the tenth year anyway, then the threat of not
cooperating in the future is completely ineffective. Hence in the ninth year, each
firm will reason that it pays to cheat on the collusive agreement by producing more
than the agreed-on amount. Collusion breaks down in the ninth year. As they reason
278 ∂ CHAPTER 12 MONOPOLY, MONOPOLISTIC COMPETITION, AND OLIGOPOLY