Volunteer's dilemma

The volunteer's dilemma is a game that models a situation in which each player can either make a small sacrifice that benefits everybody, or instead wait in hope of benefiting from someone else's sacrifice.

One example is a scenario in which the electricity supply has failed for an entire neighborhood. All inhabitants know that the electricity company will fix the problem as long as at least one person calls to notify them, at some cost. If no one volunteers, the worst possible outcome is obtained for all participants. If any one person elects to volunteer, the rest benefit by not doing so.^[1]

A public good is only produced if at least one person volunteers to pay an arbitrary cost. In this game, bystanders decide independently on whether to sacrifice themselves for the benefit of the group. Because the volunteer receives no benefit, there is a greater incentive for freeriding than to sacrifice oneself for the group. If no one volunteers, everyone loses. The social phenomena of the bystander effect and diffusion of responsibility heavily relate to the volunteer's dilemma.^{[citation needed]}

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Payoff matrix

The payoff matrix for the game is shown below:

Volunteer's dilemma payoff matrix (example)
Others Player 1	at least one cooperates	all defect
cooperate	0	0
defect	1	-10

When the volunteer's dilemma takes place between only two players, the game gets the character of the game "chicken". As seen by the payoff matrix, there is no dominant strategy in the volunteer's dilemma. In a mixed-strategy Nash equilibrium, an increase in N players will decrease the likelihood that at least one person volunteers, which is consistent with the bystander effect.

Examples in real life

The murder of Kitty Genovese

The story of Kitty Genovese is often cited as an example of the volunteer's dilemma. Genovese was stabbed to death outside her apartment building in Queens, New York, in 1964. According to a highly influential New York Times account, dozens of people witnessed the assault but did not get involved because they thought others would contact the police anyway and did not want to incur the personal cost of getting involved.^[2] Subsequent investigations have shown the original account to have been unfounded, and although it inspired sound scientific research, its use as a simplistic parable in psychology textbooks has been criticized.^[3]

The meerkat

The meerkat exhibits the volunteer's dilemma in nature. One or more meerkats act as sentries while the others forage for food. If a predator approaches, the sentry meerkat lets out a warning call so the others can burrow to safety. However, the altruism of this meerkat puts it at risk of being discovered by the predator.

References

^ Poundstone, William (1993). Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb. New York: Anchor Books. ISBN 978-0-385-41580-4.
^ Weesie, Jeroen (1993). "Asymmetry and Timing in the Volunteer's Dilemma". Journal of Conflict Resolution. 37 (3): 569–590. doi:10.1177/0022002793037003008. JSTOR 174269.
^ Manning, R.; Levine, M; Collins, A. (September 2007). "The Kitty Genovese murder and the social psychology of helping: The parable of the 38 witnesses". American Psychologist. 62 (6): 555–562. CiteSeerX 10.1.1.210.6010. doi:10.1037/0003-066X.62.6.555. PMID 17874896.

v t e Topics in game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand
Strategies	Backward induction Bid shading Collusion Forward induction Grim trigger Markov strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Bargaining problem Cheap talk Global game Intransitive game Mean-field game Mechanism design n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Stackelberg competition Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers Tic-tac-toe Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Miscellaneous	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory First-move advantage in chess Game Description Language Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions

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