Figure 3. Left panel shows the fraction of ordinary people in dependence on the temptation/loss β, as obtained for the three-strategy spatial inspection game with uniform punishment and the five-strategy spatial inspection game with heterogeneous punishment (see legend).

It can be observed that heterogeneous punishment is indeed more effective in eliminating second-order free-riding by ordinary people than uniform punishment. Right panel shows the fraction of punishers in dependence on the temptation/loss β for the uniform punishment model and the aggregate fraction of all punishers in the heterogeneous punishment model, as well as the fraction of punishers L, M and H individually (see legend). The success of heterogeneous punishment to eliminate second-order free-riding is somewhat relativized, as higher punishment levels will not necessarily lead to lower criminal levels (see Fig. 4 for an explanation). The origin of the zig-zag outlay of the aggregate fraction of all punishers is analyzed in Fig. 5. In both panels the punishment cost is α = 0.5 and the reward for punishing criminals is γ = 1.5.