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Valuation monotonicity, fairness and stability in assignment problems

René van den Brink (), Marina Núñez () and Francisco Robles ()
Additional contact information
René van den Brink: VU University and Tinbergen Institute
Francisco Robles: Universidad Carlos III de Madrid

No 2018/378, UB Economics Working Papers from Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics

Abstract: In this paper, we investigate the possibility of having stable rules for two- sided markets with transferable utility, that satisfy some valuation monotonicity and fairness axioms. Valuation fairness requires that changing the valuation of a buyer for the object of a seller leads to equal changes in the payoffs of this buyer and seller. This is satisfied by the Shapley value, but is incompatible with stability. A main goal in this paper is to weaken valuation fairness in such a way that it is compatible with stability. It turns out that requiring equal changes only for buyers and sellers that are matched to each other before as well as after the change, is compatible with stability. In fact, we show that the only stable rule that satisfies weak valuation fairness is the well-known fair division rule which is obtained as the average of the buyers-optimal and the sellers-optimal payoff vectors. Our second goal is to characterize these two extreme rules by valuation monotonicity axioms. We show that the buyers-optimal (respectively sellers-optimal) stable rule is char- acterized as the only stable rule that satisfies buyer-valuation monotonicity which requires that a buyer cannot be better off by weakly decreasing his/her valuations for all objects, as long as he is assigned the same object as before (respectively object-valuation antimonotonicity which requires that a buyer cannot be worse off when all buyers weakly decrease their valuations for the object that is assigned to this specific buyer, as long as this buyer is assigned the same object as before). Finally, adding a consistency axiom, the two optimal rules are characterized in the general domain of allocation rules for two-sided assignment markets with a variable population.

Keywords: Assignment problem; valuation monotonicity; valuation fairness; stability; fair division rules; optimal rules. (search for similar items in EconPapers)
JEL-codes: C71 C78 D63 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2018
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