# 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[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 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

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