Abstract
It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer's dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten's (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.
Highlights
In social groups, voluntary acts play a critical role in the maintenance and evolution of cooperation [1,2,3,4,5]
The volunteer’s dilemma (VD) is an N-person, binary-choice game designed to explain why the participants would be inclined to pay the cost of providing a public good shared by every individual in a social group [7,15,16,17,18]
We present an evolutionary game that describes how the frequencies of strategies within a population change in time according to the success of different strategists [42,43,44], and explore which equilibrium will survive over evolutionary time
Summary
Voluntary acts play a critical role in the maintenance and evolution of cooperation [1,2,3,4,5]. The fact that the two-person game model loses generality might be what raises the difficulty of Selten’s (1980) model in explaining why public goods are produced by the ‘‘weak’’ players in some cooperative systems. We find the evolutionarily stable strategy (ESS) of the asymmetric volunteer’s dilemma, and describe the conditions how the public good is produced by both ‘‘strong’’ and ‘‘weak’’ players in an asymmetric game.
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