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Abstract
The public goods game represents a straightforward generalization of the prisoner's
dilemma to an arbitrary number of players. Since the dominant strategy is to defect,
both classical and evolutionary game theory predict the asocial outcome that no player
contributes to the public goods. In contrast to the compulsory public goods game,
optional participation provides a natural way to avoid deadlocks in the state of mutual
defection. The three resulting strategies--collaboration or defection in the public
goods game, as well as not joining at all--are studied by means of a replicator dynamics,
which can be completely analysed in spite of the fact that the payoff terms are nonlinear.
If cooperation is valuable enough, the dynamics exhibits a rock-scissors-paper type
of cycling between the three strategies, leading to sizeable average levels of cooperation
in the population. Thus, voluntary participation makes cooperation feasible. But for
each strategy, the average payoff value remains equal to the earnings of those not
participating in the public goods game.