The evolution of altruism in spatial threshold public goods games via an insurance mechanism

The persistence of cooperation in public goods situations has become an important puzzle for researchers. This paper considers the threshold public goods games where the option of insurance is provided for players from the standpoint of diversification of risk, envisaging the possibility of multiple strategies in such scenarios. In this setting, the provision point is defined in terms of the minimum number of contributors in one threshold public goods game, below which the game fails. In the presence of risk and insurance, more contributions are motivated if (1) only cooperators can opt to be insured and thus their contribution loss in the aborted games can be (partly or full) covered by the insurance; (2) insured cooperators obtain larger compensation, at lower values of the threshold point (the required minimum number of contributors). Moreover, results suggest the dominance of insured defectors who get a better promotion by more profitable benefits from insurance. We provide results of extensive computer simulations in the realm of spatial games (random regular networks and scale-free networks here), and support this study with analytical results for well-mixed populations. Our study is expected to establish a causal link between the widespread altruistic behaviors and the existing insurance system