The Prisoners’ Dilemma (PD) and its applications

Разделы Иностранные языки •Экономико-математическое моделирование
Тип

Рефераты

Формат Microsoft Word
Язык Английский
Загрузить архив:
Файл: ref-24412.zip (10kb [zip], Скачиваний: 62) скачать

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

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 notobtain 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

[vii] Heylighen, F. (1995), The Prisoners' Dilemma, Principia Cybernetica Web, 1995, , assessed: 5.11.04 at 18:30 and Heylighen F. (1992): "Evolution, Selfishness and Cooperation", Journal of Ideas, Vol 2, # 4, pp 70-76.