筑波大学システム情報工学研究科                            

 

         平成16年度  ファカルティー・セミナー   

                       (Faculty Seminar)

 

 

日 時 : 200478()  14001500

場 所 : 第三学群B棟 3B 413

講演者 : 坂井 豊貴  [ University of Rochester大学院Ph.Dコース3 ]

司会者 : 焼田 党

演 題    Fairness and implementability in allocation of indivisible objects

                with monetary compensations

 

 

 

                           abstract

 

This paper introduces a general framework for the fair allocation of indivisible objects when each agent can consume at most one (e.g., jobs, rooms, tickets, positions, rights), and monetary compensations are possible. This framework allows several identical objects to exist and preferences to share similarity in evaluating objects. Various different models that have been discussed separately so far are unified by our model (e.g., Alkan, Demange, and Gale, 1991; Tadenuma and Thomson, 1991, 1993; Maniquet, 2003).

 

A social choice correspondence, or simply a solution, is a correspondence that maps each preference profile to a non-empty set of allocations. Our fairness requirement on solutions, called equal treatment of equals, states that two agents with identical preferences should receive consumption bundles being indifferent. We show that the no-envy solution is the unique Nash implementable solution satisfying equal treatment of equals and a mild continuity property. Furthermore, the same result holds if the continuity property is replaced by a neutrality property. These continuity and neutrality properties are so weak that they are satisfied by all standard solutions. Hence, our result suggests that, whenever we require the horizontal equity of equal treatment of equals and Nash implementability, there is essentially no other choice than the no-envy solution. Since no-envy implies Pareto efficiency in the present model, our result is perfectly compatible to Pareto efficiency. Our result is the first axiomatization of the no-envy solution in fair allocation theory.