The dynamics of public goods

Christoph Hauert; Nina Haiden; Karl Sigmund

doi:10.3934/dcdsb.2004.4.575

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2004, Volume 4, Issue 3: 575-587. Doi: 10.3934/dcdsb.2004.4.575

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The dynamics of public goods

1.
Departments of Zoology and Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z4
2.
Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna

Received: November 30, 2002

Revised: September 30, 2003

Published: July 2005

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Abstract

We analyze the replicator equation for two games closely related with the social dilemma occurring in public goods situations. In one case, players can punish defectors in their group. In the other case, they can choose not to take part in the game. In both cases, interactions are not pairwise and payoffs non-linear. Nevertheless, the qualitative dynamics can be fully analyzed. The games offer potential solutions for the problem of the emergence of cooperation in sizeable groups of non-related individuals -- a basic question in evolutionary biology and economics.

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Mathematics Subject Classification: 91A06, 91A10, 91A22, 92D25.

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