Volunteering in public goods games


by Christoph Hauert, Version 1.0, April 2002.

The evolution of cooperation among non-related individuals is one of the fundamental problems in biology and social sciences. Reciprocal altruism fails to provide a solution if interactions are not repeated often enough or groups are too large. Punishment and reward can be very effective but require that defectors can be traced and identified. Here we present a simple but effective mechanism operating under full anonymity. Optional participation can foil exploiters and overcome the social dilemma. In voluntary public goods interactions, cooperators and defectors will coexist. We show that this result holds under very diverse assumptions on population structure and adaptation mechanisms. Thus, voluntary participation offers an escape hatch out of some social traps. Cooperation can subsist in sizeable groups even if interactions are not repeated, defectors remain anonymous, players have no memory and assortement is purely random.

This work was originally published as Hauert, Ch., De Monte, S., Hofbauer, J. & Sigmund, K. (2002) Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games, Science 296, 1129-1132 (click on title to access the article online).

Further upcoming work on public goods games in different geometries:

The following pages are designed as additional material to these articles and meant as an interactive tutorial taking advantage of Java applets to visualize and experiment with the system's dynamics for parameter settings of your choice.


 

Public goods games


In a typical setup in experimental economics an experimenter endows e.g. six players with $10 each. The players are then offered to invest their money into a common pool knowing that the experimeter will triple the amount in the pool and distribute it equally among all participants irrespective of their contributions. If all players cooperate and contribute their $10, they will end up with $30 each. However, each player faces the temptation to defect and to free-ride on the other player's contributions since each invested dollar yields only a return of 50 cents to the investor. Therefore the 'rational' and dominating solution is to defect and invest nothing. Consequentially, groups of rational players will forego the public good and are thus unable to increase their initial endowment. This results in a deadlock of mutual defection and economic stalemate.

Such public goods interactions are abundant in human and animal societies. Consider for example predator inspection behavior, alarm calls and group defense as well as health insurrance, public transportation, the fight against crime or environmental issues, to name only a few.


 

Voluntary participation


Most theoretical and experimental studies on public goods games or the related prisoner's dilemma have tacitly built on the fact that the participants are actually prisoners, i.e. they are trapped in the dilemma. In nature, however, animals and humans often have, at least to a certain extend, the freedom to decide whether to participate in a public enterprise.

For this reason we extend the public goods game to allow for voluntary participation. Individuals unwilling to participate are termed loners. They prefer autarky and rather rely on some small but fixed payoff. The loner strategy is thus risk averse. But, the option to withdraw from social or economic enterprises efficiently avoids deadlocks in states of mutual defection and economic stalemate.

In the following we thus consider three strategical types: (i) cooperators and (ii) defectors both willing to join the public goods game, with different intentions though, and (iii) loners that refuse to participate. These strategies lead to a rock-scissors-paper dynamics with cyclic dominance: if cooperators abound, they can be exploited by defectors, but if defectors prevail it is best to abstain and if no one participates, small groups can form and it pays to return to cooperation.


 

Population structure


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Well-mixed populations

In well-mixed populations the potential participants in the public goods game are randomly selected.
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Rigid population structures

In order to model spatially extended systems, we consider players arranged on regular lattices. They interact only with their nearest neighbors.


 

Acknowledgements


For the development of these pages help and advice of the following two people was of particular importance: First, my thanks go to Karl Sigmund for helpful comments on the game theoretical parts and second, my thanks go to Urs Bill for introducing me into the Java language and for his patience and competence in answering my many technical questions.
Financial support of the Swiss National Science Foundation is gratefully acknowledged.


 

Updated on Monday, August 5, 2002 by Christoph Hauert. Visitors since January 2003: