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The prisoners' dilemma is the best-known game of strategy
in social science. It helps us understand what governs the balance
between cooperation and competition in business, in politics, and
in social settings.
In
the traditional version of the game, the police have arrested two
suspects and are interrogating them in separate rooms. Each can
either confess, thereby implicating the other, or keep silent. No
matter what the other suspect does, each can improve his own
position by confessing. If the other confesses, then one had better
do the same to avoid the especially harsh sentence that awaits a
recalcitrant holdout. If the other keeps silent, then one can
obtain the favorable treatment accorded a state's witness by
confessing. Thus, confession is the dominant
strategy for each. But when both confess, the
outcome is worse for both than when both keep silent. The concept
of the prisoners' dilemma was developed by Rand Corporation
scientists Merrill Flood and Melvin Dresher and was formalized by a
Princeton mathematician, Albert W. Tucker.
The
prisoners' dilemma has applications to economics and business.
Consider two firms, say Coca-Cola and Pepsi, selling similar
products. Each must decide on a pricing strategy. They best exploit
their joint market power when both charge a high price; each makes
a profit of $10 million per month. If one sets a competitive low
price, it wins a lot of customers away from the rival. Suppose its
profit rises to $12 million, and that of the rival falls to $7
million. If both set low prices, the profit of each is $9 million.
Here, the low-price strategy is akin to the prisoner's confession,
and the high-price akin to keeping silent. Call the former
cheating, and the latter cooperation. Then cheating is each firm's
dominant strategy, but the result when both "cheat" is worse for
each than that of both cooperating.
Arms
races between superpowers or local rival nations offer another
important example of the dilemma. Both countries are better off
when they cooperate and avoid an arms race. Yet the dominant
strategy for each is to arm itself heavily.
On a
superficial level the prisoners' dilemma appears to run counter to
Adam Smith's idea of the invisible hand. When each person in the
game pursues his private interest, he does not promote the
collective interest of the group. But often a group's cooperation
is not in the interests of society as a whole. Collusion to keep
prices high, for example, is not in society's interest because the
cost to consumers from collusion is generally more than the
increased profit of the firms. Therefore companies that pursue
their own self-interest by cheating on collusive agreements often
help the rest of society. Similarly cooperation among prisoners
under interrogation makes convictions more difficult for the police
to obtain. One must understand the mechanism of cooperation before
one can either promote or defeat it in the pursuit of larger policy
interests.
Can
"prisoners" extricate themselves from the dilemma and sustain
cooperation when each has a powerful incentive to cheat? If so,
how? The most common path to cooperation arises from repetitions of
the game. In the Coke—Pepsi example, one month's cheating gets the
cheater an extra $2 million. But a switch from mutual cooperation
to mutual cheating loses $1 million. If one month's cheating is
followed by two months' retaliation, therefore, the result is a
wash for the cheater. Any stronger punishment of a cheater would be
a clear deterrent.
This
idea needs some comment and elaboration:
1.
The cheater's reward comes at once, while the loss from punishment
lies in the future. If players heavily discount future payoffs,
then the loss may be insufficient to deter cheating. Thus,
cooperation is harder to sustain among very impatient players
(governments, for example).
2.
Punishment won't work unless cheating can be detected and punished.
Therefore, companies cooperate more when their actions are more
easily detected (setting prices, for example) and less when actions
are less easily detected (deciding on nonprice attributes of goods,
such as repair warranties). Punishment is usually easier to arrange
in smaller and closed groups. Thus, industries with few firms and
less threat of new entry are more likely to be
collusive.
3.
Punishment can be made automatic by following strategies like "tit
for tat," which was popularized by University of Michigan political
scientist Robert Axelrod. Here, you cheat if and only if your rival
cheated in the previous round. But if rivals' innocent actions can
be misinterpreted as cheating, then tit for tat runs the risk of
setting off successive rounds of unwarranted
retaliation.
4. A
fixed, finite number of repetitions is logically inadequate to
yield cooperation. Both or all players know that cheating is the
dominant strategy in the last play. Given this, the same goes for
the second-last play, then the third-last, and so on. But in
practice we see some cooperation in the early rounds of a fixed set
of repetitions. The reason may be either that players don't know
the number of rounds for sure, or that they can exploit the
possibility of "irrational niceness" to their mutual
advantage.
5.
Cooperation can also arise if the group has a large leader, who
personally stands to lose a lot from outright competition and
therefore exercises restraint, even though he knows that other
small players will cheat. Saudi Arabia's role of "swing producer"
in the OPEC cartel is an instance of this.
囚徒困境看起来简单的博弈模型（故事），其实都反映了一类社会现象背后的结构。还有更多的博弈故事都可以和经济有所联系。
囚徒困境反映了个人理性与集体理性的冲突；智猪博弈反映了搭便车问题；懦夫博弈反映了人们在利益完全冲突中的骑虎难下之困局；性别战则反映了参与人具有局部的共同利益下的行为协调；猎鹿博弈则反映了参与人具有完全的共同利益下的行为协调……在这些模型中，赢利数字本身是多少并不重要，关键是赢利数字满足了一种特定的结构，对应解释了一种特定社会现象的形成机理。
About the
Authors
Avinash Dixit and
Barry Nalebuff ：
Avinash Dixit is
the John J. Sherred Professor of Economics at Princeton University.
Barry Nalebuff is the Milton Steinbach Professor of Management at
Yale University's School of Organization and
Management. |
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