The Prisoners’ Dilemma (PD) and its applications
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[i])
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:[ii]
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’[iii],
but what governs the balance between cooperation and competition? For example,
the production decision of two members (Iran and Iraq) of the OPEC[iv] 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
|
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.[v] 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.[vi]
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.[vii]
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.
[i] Axelrod, R. (1984), The Evolution of Cooperation, p. 17
[ii] Barret, S. (2003), Environment and Statecraft – The Strategy of
Environmental Treaty-making, Oxford University Press, pp. 53-54
[iii] Brandenburg, Adam M. and Barry J. Nalebuff (1996), Co-opetition , New York, p.4
[iv] 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
[v] 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
[vi] Axelrod, R. (1984), p. 33