On recursive solutions to simple allocation problems

Abstract

We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment E among n agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision processwhere the policy-maker initially starts with a reference allocation of E in mind and then uses the data of the problem to recursively adjust his previous allocation decisions.We showthat recursive rules uniquely satisfy rationality, c-continuity, and other-c monotonicity. We also show that a well-known member of this class, the Equal Gains rule, uniquely satisfies rationality, c-continuity, and equal treatment of equals.