Combination of institutional incentives for cooperative governance of risky commons

Abstract

Finding appropriate incentives to enforce collaborative efforts for governing the commons in risky situations is a long-lasting challenge. Previous works have demonstrated that both punishing free-riders and rewarding cooperators could be potential tools to reach this goal. Despite weak theoretical foundations, policy makers frequently impose a punishment-reward combination. Here, we consider the emergence of positive and negative incentives and analyze their simultaneous impact on sustaining risky commons. Importantly, we consider institutions with fixed and flexible incentives. We find that a local sanctioning scheme with pure reward is the optimal incentive strategy. It can drive the entire population toward a highly cooperative state in a broad range of parameters, independently of the type of institutions. We show that our finding is also valid for flexible incentives in the global sanctioning scheme, although the local arrangement works more effectively.

Keywords: Decision science; Global change; Nature conservation; Social sciences.

Graphical abstract

Figure 1

Evolutionary dynamics of cooperators, defectors, and executors under local scheme with fixed incentives Here, the risk level is r = 0.2. In panel A, in the extreme case of $\alpha =1$, E becomes equivalent to a pure rewarding strategy, while the other extreme case of $\alpha =0$, where E is a pure punisher, can be seen in panel B. The darker dots in the simplex represent the regions where the population spends more time. Orange arrows represent the most likely direction of evolution when the population leaves the current configuration, obtained by computing the gradient of selection. We set the collective target M to $75\text{\%}$ of the group size. Local scheme is established when the number of executors exceeds 25$\text{\%}$ of the group. Parameter values are Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and ${\pi }_e=0.3$.

Figure 2

The average group achievement ${\eta }_G$ under local scheme with fixed incentives Panel A shows ${\eta }_G$ as a function of α for three different values of r. The inset of panel A shows ${\eta }_G$ as a function of α, where the value of α ranges from 0.4 to 1.0. Panel B shows ${\eta }_G$ as a function of r in the cases without incentive strategy E and with three different weight factor values in its presence. Panel C shows ${\eta }_G$ as a function of μ for three different values of α. The inset of panel c shows ${\eta }_G$ as a function of μ, where the value of μ ranges from 0.001 to 0.01. Parameter values are Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and ${\pi }_e=0.3$ in panels A and B; Z = 100, N = 4, c = 0.1, b = 1, r = 0.3, ${\pi }_t=0.03$, and ${\pi }_e=0.3$ in panel C.

Figure 3

The institution prevalence ${\eta }_I$ and the average reward and fine under local scheme with fixed incentives Panel A shows ${\eta }_I$ as a function of α for three different values of r. Panel B shows the average fine on defectors and the average reward on cooperators and executors as a function of α. Parameter values are Z = 100, N = 4, c = 0.1, b = 1, μ = 1/Z, π_t = 0.03, and π_e = 0.3 in panel A; Z = 100, N = 4, c = 0.1, b = 1, r = 0.2, μ = 1/Z, π_t = 0.03, and π_e = 0.3 in panel B.

Figure 4

Evolutionary dynamics of cooperator, defector, and executor strategy under local scheme with flexible incentives The risk level is r = 0.35. Panels A and C show the case of pure reward ($\alpha =1$). Panels B and D show the case of pure punishment ($\alpha =0$). Parameter values are Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and $\delta =1.4$ in panels A and B; Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and $\delta =3$ in panels C and D.

Figure 5

The average group achievement ${\eta }_G$ under local scheme with flexible incentives Panel A shows η_G as a function of α for three different values of δ. Panel B shows η_G as a function of r in the cases without incentive strategy E and with three different values of α. Panel C shows η_G as a function of δ for three different values of α. Panel D shows η_G as a function of μ for three different values of α. Parameter values are Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and r = 0.2 in panel Α; Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and $\delta =2$ in panel Β; Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and r = 0.5 in panel C; Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, r = 0.2, and $\delta =3$ in panel D.

Figure 6

The institution prevalence ${\eta }_I$ and the average reward and fine under local scheme with flexible incentives Parameter values are Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, ${\pi }_t=0.03$, and r = 0.2 in panel A; Z = 100, N = 4, c = 0.1, b = 1, $\mu =1/Z$, $\delta =3$, ${\pi }_t=0.03$, and r = 0.2 in panel B.