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The Prisoners Dilemma (PD) and its applications ()
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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)

 

Irans Output

 

Iraqs 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 players 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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