Allocation of Common-Pool Resources in an Unmonitored Open System

In an open system, system resources are managed by the contributors themselves. Because the participation needs to be voluntary and contributors true utility will remain unmonitored, proper communication among the participants is essential. In the discussed common-pool resource (CPR) problem, all the members need not be contributors, but the non-excludable component of the resource is required to be multiplied with each of the member's rivalrous component, and all these products are needed to be summed up to calculate the overall resource requirement. This characteristic applies to a typical power system optimization problem, where, if a customer group installs a common dynamic voltage restorer, voltage improvement can be treated as non-excludable quantity, while the peak load of individual customers can be treated as rivalrous quantity. In this work, we consider, the participants sharing the CPR contribute to form an open system to capitalize on `economy of scale', while discouraging the unilateral free-riding benefit. Considering the benefit and average production cost curve represented by piecewise linear functions we have shown that the utility function is convex. Furthermore, for the given problem, we have numerically calculated the utility distribution scheme by solving an optimization problem.