Resource Allocation Problems with Concave Reward Functions

Abstract: In a resource allocation problem there is a common-pool resource, which has to be divided among agents. Each agent is characterized by a claim on this pool and an individual concave reward function on assigned resources. An assignment of resources is optimal if the total joint reward is maximized. We provide a necessary and sufficient condition for optimality of an assignment. Analyzing the associated allocation problem of the maximal total joint reward, we consider corresponding resource allocation games. It is shown that these games have a non-empty core and thus allow for stable allocations. Moreover, an explicit expression for the nucleolus of these games is provided.