Excessive abundance of common resources deters social responsibility - PubMed (original) (raw)

Excessive abundance of common resources deters social responsibility

Xiaojie Chen et al. Sci Rep. 2014.

Abstract

We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions. All players initially receive endowments from the available amount of common resources. While cooperators contribute part of their endowment to the collective target, defectors do not. If the target is not reached, the endowments of all players are lost. In our model, we introduce a feedback between the amount of common resources and the contributions of cooperators. We show that cooperation can be sustained only if the common resources are preserved but never excessively abound. This, however, requires a delicate balance between the amount of common resources that initially exist, and the amount cooperators contribute to the collective target. Exceeding critical thresholds in either of the two amounts leads to loss of cooperation, and consequently to the depletion of common resources.

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Figures

Figure 1

Figure 1. Socially responsible actions are viable even if the common resources are initially scarce, as long as the common pool is subsequently kept properly filled.

Either too low or too abundant contributions, or failure to distribute them in time, can lead to the tragedy of the commons. Colour maps encode the fraction of cooperators ρc in dependence on the multiplication factor α and the initial amount of common resources available to each group R, for three different values of the maximal endowment b: (a) 5, (b) 10, and (c) 20.

Figure 2

Figure 2. Sustainability of common resources is achieved by socially responsible actions.

Only an intermediate contribution strength, combined with initially scarce resources, leads to sustainable common resources. In panel (a) the colour map encodes the fraction of groups where the resources can be sustained [i.e., Ri(∞) > 0], while in panel (b) the colour map encodes the fraction of groups where the cumulative common goods can provide enough endowments [i.e., Ri(∞) ≥ _Gb_] for all involved. For results in both panels we use the maximal endowment b = 10.

Figure 3

Figure 3. Spatial patterns explain why an excessive abundance of common resources deters social responsibility.

Blue (yellow) are cooperators (defectors) that are central to groups where the common resources abound, while green (red) are cooperators (defectors) that are central to groups where the common resources are scarce. Grey denotes defectors where the common resources are completely depleted. Top row show the time evolution (from left to right) for α = 1, b = 10, and R = 50. Due to the low multiplication factor the common resources vanish fast. Middle row shows the time evolution for α = 10, b = 10, and R = 50. Here only cooperative groups succeed in keeping the pool from emptying. Groups with defectors quickly become unsustainable and hence pave the way towards cooperator dominance. Bottom row show the time evolution for α = 20, b = 10, and R = 50. Due to the high value of α common resources start to abound excessively, making even predominantly defective groups sustainable and thus fit to invade cooperators.

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