Rewards and the private provision of public goods on dynamic networks

We study an evolutionary model of a public good game with rewards played on a network. Giving rewards to contributors transforms the game but gives rise to a second-order dilemma. By allowing for coevolution of strategies and network structure, the evolutionary dynamics operate on both structure and strategy. Players learn with whom to interact and how to act and can overcome the second-order dilemma. More specifically, the network represents social distance which changes as players interact. Through the change in social distance, players learn with whom to interact, which we model using reinforcement dynamics. We find that, for certain parameter constellations, a social institution, prescribing prosocial behavior and thus solving the second-order dilemma, can emerge from a population of selfish players. Due to the dynamic structure of the network, the institution has an endogenous punishment mechanism ensuring that defectors will be excluded from the benefits of the institution and the public good will be supplied efficiently.