Sharing rules for a common-pool resource with private alternatives

Agents with ex-ante claims over a common pool resource (CPR) of uncertain size face the risk of resource shortage if the sum of the claims they have over the common pool resource is incompatible with the actual resource size. In case of shortage, a sharing rule or bankruptcy rule is required to organize the restrictions and allocate the available resource among CPR users. However, in many situations, agents can diversify their resources and substitute an alternative safe but costly resource to the free but risky CPR. Optimal resource management requires to study the interaction between the sharing rule of the CPR and the resource diversification choices of agents. We find the optimal sharing rule under two assumptions concerning the regulator: i) the social planner defines simultaneously the sharing rule and the diversification choices in order to maximize social welfare; ii) the policy maker uses the sharing rule as an instrument to induce and each agent to make the optimal diversification decision. We interpret our results in the context of water management in France.