COEXISTENCE OF COOPERATION AND DEFECTION IN PUBLIC GOODS GAMES
Article first published online: 1 DEC 2010
© 2010 The Author(s). Evolution© 2010 The Society for the Study of Evolution.
Volume 65, Issue 4, pages 1140–1148, April 2011
How to Cite
Archetti, M. and Scheuring, I. (2011), COEXISTENCE OF COOPERATION AND DEFECTION IN PUBLIC GOODS GAMES. Evolution, 65: 1140–1148. doi: 10.1111/j.1558-5646.2010.01185.x
- Issue published online: 4 APR 2011
- Article first published online: 1 DEC 2010
- Accepted manuscript online: 10 NOV 2010 02:10AM EST
- Received May 30, 2010, Accepted November 1, 2010
- game theory;
- mixed equilibrium;
- prisoner's dilemma;
- public good;
- volunteer's dilemma
The production of public goods by the contribution of individual volunteers is a social dilemma because an individual that does not volunteer can benefit from the public good produced by the contributions of others. Therefore it is generally believed that public goods can be produced only in the presence of repeated interactions (which allow reciprocation, reputation effects and punishment) or relatedness (kin selection). Cooperation, however, often occurs in the absence of iterations and relatedness. We show that when the production of a public good is a Volunteer's Dilemma, in which a fixed number of cooperators is necessary to produce the public good, cooperators and defectors persist in a mixed equilibrium, without iterations and without relatedness. This mixed equilibrium is absent in the N-person Prisoner's Dilemma, in which the public good is a linear function of the individual contributions. We also show that the Prisoner's Dilemma and the Volunteer's Dilemma are the two opposite extremes of a general public goods game, and that all intermediate cases can have a mixed equilibrium like the Volunteer's Dilemma. The coexistence of cooperators and defectors, therefore, is a typical outcome of most social dilemmas, which requires neither relatedness nor iterations.