Decentralized incentives for general well-being in networked public goods game

Prosocial incentives are recognized as effective tools to promote public cooperation. But their usage is costly, hence we need find an optimal policy that offers the best outcome for a minimal cost. This problem has attracted extensive attention of scholars from many fields, and it been studied intensively in well-mixed populations. Yet, system behavior case group interactions where decentralized involved rather unexplored. To fill this gap, consider possible consequences rewarding punishing spatially arranged population players play goods game with neighbors. Importantly, both time-independent dynamically varying cases checked. With help pair approximation approach, derive dynamical equations under weak selection obtain theoretical conditions minimally requested amounts expected outcome. By using control theory, also devise index function quantify executing costs protocols. In addition, numerical calculations Monte Carlo simulations support scheme requires lower cumulative cost than alternative if initial cooperation level below threshold value. Otherwise, punishment more efficient.