Serial dictatorship vs. Nash in assessing Pareto optimality in many-to-many matchings with an application in water management

Abstract

This paper examines and compares mechanisms for finding Pareto optimal solutions to a many-to-many allocation problem. By explicitly introducing preference ordering and providing linear programming representations of the allocation problem, we study serial dictatorship and competitive matching with simultaneous choices, which is basically a generalized Nash equilibrium problem, and show that under certain conditions this Nash equilibrium allocation is also Pareto optimal. We examine the ability of our mechanisms to provide Pareto optimal allocations, and compare the solutions obtained from the different mechanisms. In addition, the allocation methods are applied to a many-sources, many-users water allocation problem, and the benefits associated with serial dictatorship or competitive allocations are compared.