title: Probabilistic participation in public goods games.
abstract: Voluntary participation in public goods games (PGGs) has turned out to be a simple but effective mechanism for promoting cooperation under full anonymity. Voluntary participation allows individuals to adopt a risk-aversion strategy, termed loner. A loner refuses to participate in unpromising public enterprises and instead relies on a small but fixed pay-off. This system leads to a cyclic dominance of three pure strategies, cooperators, defectors and loners, but at the same time, there remain two considerable restrictions: the addition of loners cannot stabilize the dynamics and the time average pay-off for each strategy remains equal to the pay-off of loners. Here, we introduce probabilistic participation in PGGs from the standpoint of diversification of risk, namely simple mixed strategies with loners, and prove the existence of a dynamical regime in which the restrictions ono longer hold. Considering two kinds of mixed strategies associated with participants (cooperators or defectors) and non-participants (loners), we can recover all basic evolutionary dynamics of the two strategies: dominance; coexistence; bistability; and neutrality, as special cases depending on pairs of probabilities. Of special interest is that the expected pay-off of each mixed strategy exceeds the pay-off of loners at some interior equilibrium in the coexistence region.
authors: Graduate School of Engineering, Soka University, Tokyo, Japan. tsasaki@soka.ac.jp
authors: Tatsuya
authors: T
authors: Sasaki
authors: Isamu
authors: I
authors: Okada
authors: Tatsuo
authors: T
authors: Unemi
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D006126:Group Processes; D006801:Humans; D008954:Models, Biological; D011336:Probability; D017150:Public Sector
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