Consistency and monotonicity in assignment problems

This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem the paper uses six axioms including the consistency and the weak pairwise-monotonicity which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problem coincides with the set of the competitive allocations of the economy, the present characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, the main result gives a new normative implication of competitive equilibria.