Competition of individual and institutional punishments in spatial public goods games

TL;DR

This study explores how individual and institutional punishments influence strategy evolution in spatial public goods games, revealing complex interactions, dominance conditions, and the potential for mutual extinction of punishments leading to defector victory.

Contribution

It provides a detailed numerical analysis of the interplay between peer and pool punishments in spatial public goods games, highlighting conditions for their success or failure.

Findings

Peer punishers dominate in many parameter regions.

Pool punishers survive mainly under weak peer punishment.

Punishments can mutually extinguish, allowing defectors to prevail.

Abstract

We have studied the evolution of strategies in spatial public goods games where both individual (peer) and institutional (pool) punishments are present beside unconditional defector and cooperator strategies. The evolution of strategy distribution is governed by imitation based on random sequential comparison of neighbors' payoff for a fixed level of noise. Using numerical simulations we have evaluated 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.