Strategic Manipulations of Multi-Valued Solutions in Economies with Indivisibilities
Posted: 30 Jul 2004
Date Written: July 2004
Abstract
We study manipulability of multi-valued solutions in fair allocation of homogeneous indivisible objects with monetary transfers. We show that the no-envy solution satisfies some extension of strategy-proofness to multi-valued solutions. Since no-envy implies Pareto efficiency in this literature, this result implies that we can escape many impossibility results on strategy-proofness by allowing a solution to be multi-valued and extending strategy-proofness in an appropriate way. Nevertheless, we show that no-envy is not immune to all forms of manipulations. In that sense, we are able to identify what kind of manipulations occur. Next, we derive impossibility results on the egalitarian-equivalence and efficient solution. The intuition that manipulability comes from single-valuedness is not confirmed by this solution. Finally, we show that there is no subsolution of the Pareto and identical preferences lower bound satisfying the notion of extended strategy-proofness used by Tadenuma-Thomson (1995).
Keywords: Indivisible goods, Extended strategy-proofness, No-envy, Egalitarian equivalence, Identical preferences lower bound, Fair allocations
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