.

The Prisoners’ Dilemma (PD) and its applications

In the real world one can observe not only successful episodes of
cooperation in politics, business and everyday life but also
unsuccessful ones with all its negative effects. The Prisoners’ Dilemma
(PD) can explain these non-cooperated situations. The PD can be defined
as a game situation where two players have simultaneously made a
strategic choice and both end up in its worst possible outcome. The
assumptions are: 1.) both player are rational and each player knows that
all the other players are rational, meaning that both choose their
strategy according to the highest payoffs or utilities, and 2.) both
know the payoffs (at least the order of payoffs) and both know that the
opponent knows it as well.

For instance, two countries (X, Y) have to choose their emission target
simultaneously with the given payoffs in Table 1:

Table 1: Transnational Cooperation Dilemma

Country

X

Y

Abate Pollute

A (1, 1) (-1, 2)

P (2, -1) (0, 0)

Without knowing what the other country is choosing (imperfect
information) country X will choose pollute because 2 > 1 and 0 > -1.
Respectively, country Y will also choose pollute because it is its
rational choice. The dilemma is that both end up in a unique Nash
equilibrium with the payoff nil.

The PD is evident in many real life situations, for instance price
setting within a cartel or an alliance. ‘Business is cooperation when it
comes to creating a pie and competition when it comes to dividing it
up’, but what governs the balance between cooperation and competition?
For example, the production decision of two members (Iran and Iraq) of
the OPEC illustrates a prisoners’ dilemma. Both can choose between two
production levels, either 2 or 4 million barrels of crude oil a day. The
profits (measured in millions of dollars per day) are shown in Table 2:

Table 2: Table of Profits (Iran, Iraq)

Iran’s Output

Iraq’s Output

2 4

2 (46, 42) (26, 44)

4 (52, 22) (32, 24)

Again, they have to decide simultaneously without knowing what the other
is choosing. Both countries have a dominant strategy: both want to
produce at the highest level of profits. Both end up by producing 4
million barrels and earn respectively $32 and$24 million dollar per
day. The problem is to find a way where both produce at lower levels
with high prices and hence highest profits, given the temptation of
cheating and gaining at the expense of the other.

The major reason why a prisoners’ dilemma exists is the lack of
information exchange about the other player’s actions. This problem can
take various forms, which could be classified in two groups. First, the
lack of communication preconditioned by the rules of the game. In the
classical Tchaikovsky case the two prisoners could not obtain the
information because they were separated by physical boundaries of the
cells. Secondly, it is the competitive nature of the players, which is
not necessarily preconditioned by the rules of the game. In the case of
Iraq and Iran, the two countries could cooperate, but the self-interest
of the two players does not allow them to achieve the best outcome. The
applications of such a setting can be observed in business competition
as well. The dilemma can also be viewed from an interpersonal
prospective. There is experimental evidence of how people behave and
interact in a situation that potentially leads to a prisoners’ dilemma.
Scientists have distinguished two types of personalities that determine
the outcome of repeated games: cooperative and competitive ones. In
other words, the propensity of a person in a group to cooperate or to
compete determines the outcome of the game. In sum, to avoid being
trapped in a prisoners’ dilemma cooperation and/or exchange of
information is the most crucial element.

However, rules of the game might be that cooperation is not possible
(the players meet just once). What makes it possible for cooperation to
emerge is that players might meet again (iterated PD) and do not know
the end of the game. That means today’s choice not only influences the
outcome today, but can also influence the players’ choices later. Now,
trust matters and the path to success is to find patterns of cooperation
based on reciprocity.

Should the prisoners’ dilemma be resolved or not? Some would like to see
it resolved others not. In the case of law enforcement agencies that are
working against corruption one can say that a prisoners’ dilemma should
not be resolved. In the sense, criminals should not have the chance to
cooperate under interrogation. They may agree not to confess and that
would make it very difficult to prove that they are guilty. In fact,
many mafia families pursue a rule, which says not to collaborate with
the police at all.

Now, when we look at competition of airlines or any other industry it is
clear that alliances or any other form of organizations can allow a few
companies to make extraordinary high profits while the result for
customers can be higher prices. From the customers’ point of view it
would be better when there is no communication between major producers
and retailers.

The PD, a conflict between collective interests and individual
interests, in a contemporary world is often the dilemma of the interests
of a small group of business owners over the society as a whole.

In the resolution of the dilemma we look at short-term scope. Decision
making in the model usually involves short term or immediate thinking.
Whereas in real world situations companies that are involved in
artificial price agreements risk losing reputational-capital. The same
applies to examples of law enforcement agencies and the mafia. In
consideration of long term prospective, members will not confess because
if they would end up with a ‘light’ sentence the family may announce
their own sentence, while going to prison can be guarantee of a
respectful life afterwards.

The PD explains straightforward why business, politics and everyday life
situations end up in its worst possible outcome when players are trapped
in a simultaneous-move game. Under the assumption of the PD there is
even not a loophole out of the dilemma. By repeating the game trust is
going to be crucial to reach a better outcome. Nevertheless, there is no
best strategy because it depends upon what the other player is likely to
do and what he expects the other player is doing. In real life
situations PD should not always be resolved, and in fact often best
effort should be made not to allow coordination and collaboration.

Axelrod, R. (1984), The Evolution of Cooperation, p. 17

Barret, S. (2003), Environment and Statecraft – The Strategy of
Environmental Treaty-making, Oxford University Press, pp. 53-54

Brandenburg, Adam M. and Barry J. Nalebuff (1996), Co-opetition, New
York, p.4

Organization of Petroleum Exporting Countries (OPEC), example from
Dixit, Avinash K. and Barry J. Nalebuff (1991), Thinking Strategically,
The Competitive Edge in Business, Politics and Everyday Life, W. W.
Norton & Company, New York, p. 90

Andreoni, J. and J.H Miller (1993), ‘Rational Cooperation in the
Finitely Repeated Prisoner’s Dilemma: Experimental Evidence’, The
Economic Journal, (103), 418, 576-577

Axelrod, R. (1984), p. 33

“ftp://ftp.vub.ac.be/pub/projects/Principia_Cybernetica/Papers_Heylighen
/Memes&Cooperation.txt” \t “_blank” Evolution, Selfishness and
Cooperation “, Journal of Ideas, Vol 2, # 4, pp 70-76.

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21 Окт 2010
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