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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
67/2010

The tragedy of the commons in a multi-population complementarity game

Jürgen Jost and Wei Li

Abstract

We study a complementarity game with multiple populations whose members’ offered contributions are put together towards some common aim. When the sum of the players’ offers reaches or exceeds some threshold K, they each receive K minus their own offers. Else, they all receive nothing. Each player tries to offer as little as possible, hoping that the sum of the contributions still reaches K, however. The game is symmetric at the individual level, but has many equilibria that are more or less favorable to the members of certain populations. In particular, it is possible that the members of one or several populations do not contribute anything, a behavior called defecting, while the others still contribute enough to reach the threshold. Which of these equilibria then is attained is decided by the dynamics at the population level that in turn depends on the strategic options the players possess. We find that defecting occurs when more than 3 populations participate in the game, even when the strategy scheme employed is very simple, if certain conditions for the system parameters are satisfied. The results are obtained through systematic simulations.

Received:
Nov 12, 2010
Published:
Nov 15, 2010
Keywords:
Evolutionary game, Multi-population

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2010 Repository Open Access
Jürgen Jost and Wei Li

The tragedy of the commons in a multi-population complementarity game