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
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