On recursive solutions to simple allocation problems

We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$E$$</EquationSource> </InlineEquation> among <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation> agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision process where the policy-maker initially starts with a reference allocation of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$E$$</EquationSource> </InlineEquation> in mind and then uses the data of the problem to recursively adjust his previous allocation decisions. We show that 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. Copyright Springer Science+Business Media New York 2013