Volunteer's dilemma

The volunteer dilemma (English Volunteer 's dilemma ) is a problem of game theory, might be achieved through the collective profit already by a partial waiver profit of a single actor. It represents a game-theoretic formalization of the well-known from social psychology diffusion of responsibility

The 1985 by Andreas Diekmann first examined voluntary dilemma is often illustrated with the case of failing to assist in the murder of Kitty Genovese. In this murder in New York 38 witnesses observed from extending over an extended period of protracted violence of her apartment and none of the witnesses, of whom noticed the presence of every single other witnesses, provided assistance or alerted the police.

Game Theoretical considerations

When voluntary dilemma are two or more actors involved (). There is a volunteer (ie, a " cooperating " ), get all the actors involved the payment ( the benefit). A volunteer has but for meeting the cost, or the payment of the volunteers is thus obtained (based on the prisoner's dilemma referred to as Defektierende ) the hesitant to go to the payout.

If the cost of a volunteer are smaller than the individual benefit () does not exist in each case, a Nash equilibrium if a person cooperates, but the others. This equilibrium is also Pareto - optimal. However, since the equilibrium is asymmetric with symmetric initial situation, it can not be achieved without understanding or contracts. In mixed strategies, there is another Nash equilibrium, with the following probability of cooperation:

If, however, the cost of a volunteer exceed the benefits, the defection (ie doing nothing ) thus the dominant strategy and the idleness of all actors is not a Pareto optimal Nash equilibrium dar.