How Much to Share in Resource Pooling

Resource pooling between two service providers, each having a fixed number of resources is considered. Each of the providers commit some of their resources to the common pool, and use the other providers’ resources (committed by it to the common pool) if available to service their clients if all of their own resources are completely occupied. Each such request requires a fixed payment to the other provider. The standard model of exponentially distributed occupancy time for each resource request is assumed. Assuming transferable utilities, Shapley value based inter-provider payoff keeps the coalition stable, and the problem is to find the optimal number of resources to commit to the common pool by each provider that maximizes the sum of the revenues of the two service providers. An exact solution is derived for the problem that depends on the prices charged by each provider to its clients. In case of equal prices, either full sharing or no sharing is shown to be optimal. Otherwise, the service provider with lower price commits all its resources, while the other provider commits resources depending on the solution of a recursive equation.