Asymmetric interaction and diverse forms in public goods production in volunteer dilemma game

Theoretical prediction of classical evolutionary games shows that public goods is contributed either by strong players in asymmetric games or by all of the involved players in symmetric games. However, it is inconsistency with experimental observations that weak players could also contribute to public goods in real cooperation systems. To reconciling these conflicts, we here study an evolutionary volunteer's dilemma game by assuming different roles can be interchangeable. In this model, not only the existence of multiple equilibria is possible but also the evolutionary result of the system depends on initial conditions, which can be interpreted as the production modes of public goods under different circumstances. Specifically, we found that the survival of strong individuals with mixed strategies is associated with two different outcomes: one is similar to Selten's model, that is, public goods are produced by strong players if the defectors are weak players and strong defectors are scarce in the initial condition; and the other is that the weak individuals with mixed strategies produce public goods if the defectors are strong individuals, where the strong cooperators are absent in the initial condition. Moreover, the weak individuals with mixed strategies produce public goods while strong individuals mainly display defection if the cooperation of strong players is absent in the initial condition. Our main results may help to explain the emergence of diverse forms of cooperation in asymmetric evolutionary games.