The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.
COBISS.SI-ID: 18706952
Working together in groups may be beneficial if compared to isolated efforts. Yet this is true only if all group members contribute to the success. If not, group efforts may act detrimentally on the fitness of their members. Here we study the evolution of cooperation in public-goods games on scale-free networks that are subject to deletion of links connected to the highest-degree individuals, i.e., on network that are under attack. We focus on the case where all groups a player belongs to are considered for the determination of payoffs; the so-called multigroup public-goods games. We find that the effect of link deletions on the evolution of cooperation is predominantly detrimental, although there exist regions of the multiplication factor where the existence of an "optimal" number of removed links for the deterioration of cooperation can also be demonstrated. The findings are explained by means of wealth distributions and analytical approximations, confirming that socially diverse states are crucial for the successful evolution of cooperation.
COBISS.SI-ID: 18707976
Previous research has highlighted the importance of strong heterogeneity for the successful evolution of cooperation in games governed by pairwise interactions. Here we determine to what extent this is true for games governed by group interactions. We therefore study the evolution of cooperation in the public goods game on the square lattice, the triangular lattice, and the random regular graph, whereby the payoffs are distributed either uniformly or exponentially amongst the players by assigning to them individual scaling factors that determine the share of the public good they will receive. We find that uniformly distributed public goods are more successful in maintaining high levels of cooperation than exponentially distributed public goods. This is not in agreement with previous results on games governed by pairwise interactions, indicating that group interactions may be less susceptible to the promotion of cooperation by means of strong heterogeneity than originally assumed, and that the role of strongly heterogeneous states should be reexamined for other types of games.
COBISS.SI-ID: 18843144