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Replicator dynamics for optional public good games.

Christoph Hauert1, Silvia De Monte, Josef Hofbauer

  • 1Institute for Mathematics, University of Vienna, Strudlhofgasse 4, 1090, Vienna, Austria.

Journal of Theoretical Biology
|October 17, 2002
PubMed
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Optional participation in public goods games allows for cooperation. Even with nonlinear payoffs, a rock-scissors-paper dynamic emerges, promoting significant cooperation levels.

Area of Science:

  • Game Theory
  • Evolutionary Biology
  • Social Sciences

Background:

  • The public goods game, a generalization of the prisoner's dilemma, typically predicts defection as the dominant strategy, leading to no contributions.
  • Classical and evolutionary game theory predict an asocial outcome where no player contributes to public goods.

Purpose of the Study:

  • To analyze the impact of optional participation on cooperation in public goods games.
  • To investigate the dynamics of strategies including collaboration, defection, and non-participation.

Main Methods:

  • Replicator dynamics were employed to analyze the game with nonlinear payoff terms.
  • The study examined three strategies: collaboration, defection, and opting out of the public goods game.

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Main Results:

  • Optional participation offers a viable alternative to mutual defection.
  • A "rock-scissors-paper" cycling dynamic was observed between the three strategies when cooperation is sufficiently valuable.
  • This dynamic leads to substantial average cooperation levels within the population.

Conclusions:

  • Voluntary participation in public goods games can make cooperation feasible.
  • Despite potential for cooperation, the average payoff for all strategies equals that of non-participants.