Voluntary Dilemma

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

The voluntary dilemma first examined by Andreas Diekmann in 1985 is often illustrated with the case of failure to provide assistance in the murder of Kitty Genovese . In this murder in New York, 38 witnesses observed the protracted violence from their home and none of the witnesses, each of whom noticed the presence of the other witnesses, provided assistance or called the police.

Game theory consideration

There are two or more actors involved in the voluntary dilemma ( ). If a volunteer is found (that is, a "cooperating"), all actors involved receive the payment (the benefit) . However, a volunteer has to pay the costs for this , the payout of the volunteer is, however , the hesitant (based on the prisoner's dilemma also called defective ) receive the payout . ${\displaystyle n\geq 2}$ ${\displaystyle N}$ ${\displaystyle K}$ ${\displaystyle N-K}$ ${\displaystyle N}$

If a volunteer's cost is less than the individual's benefit ( ), there is a Nash equilibrium when one person cooperates but the other does not. This balance is also Pareto-optimal . However, since the equilibrium is asymmetrical in a symmetrical initial situation, it cannot be achieved without agreements or contracts. In mixed strategies there is another Nash equilibrium with the following probability of cooperation: ${\displaystyle N-K\geq 0}$

${\displaystyle p\ast =1-{\sqrt[{n-1}]{\frac {K}{N}}}}$

On the other hand, if the costs for a volunteer exceed the benefit, defection (i.e. doing nothing) becomes the dominant strategy . The inactivity of all actors thus represents a Nash equilibrium in dominant strategies. This Nash equilibrium is a Pareto optimum , since no other combination of strategies does one (or even both) of the actors better without one of the actors suffering a disadvantage.

literature

• Andreas Diekmann: Game Theory. Rowohlt Taschenbuch Verlag, Reinbek near Hamburg 2009, ISBN 978-3-499-55701-9

Individual evidence

1. ↑ Andreas Diekmann: Volunteer's Dilemma. In: Journal of Conflict Resolution. 29: 605-610, 1985
2. ^ Andreas Diekmann: Game theory. Page 122f, see literature
3. ^ Andreas Diekmann: Game theory. Page 123ff, see literature
4. ^ Andreas Diekmann: Game theory. Page 129ff, see literature