Competition of individual and institutional punishments in spatial public goods games.

We have studied the evolution of strategies in spatial public goods games where both individual (peer) and institutional (pool) punishments are present in addition to unconditional defector and cooperator strategies. The evolution of strategy distribution is governed by imitation based on the random sequential comparison of neighbors' payoff for a fixed level of noise. Using numerical simulations, we evaluate the strategy frequencies and phase diagrams when varying the synergy factor, punishment cost, and fine. Our attention is focused on two extreme cases describing all the relevant behaviors in such a complex system. According to our numerical data peer punishers prevail and control the system behavior in a large segments of parameters while pool punishers can only survive in the limit of weak peer punishment when a rich variety of solutions is observed. Paradoxically, the two types of punishment may extinguish each other's impact, resulting in the triumph of defectors. The technical difficulties and suggested methods are briefly discussed.