Upper-contour strategy-proofness in the random assignment problem

Abstract

Bogomolnaia and Moulin (2001) showed that the mechanism that satisfies sd-efficiency and equal treatment of equals cannot be sd-strategy-proof. Also, Mennle and Seuken (2017) showed a decomposition result of strategy-proofness and presented partial strategy-proofness, which is a weak notion of strategy-proofness used by Mennle and Seuken's paper. In this paper, we show other strategy-proofness notion under the random assignment problem. In this paper, we present a weakened notion of strategy-proofness which is related to the upper-contour set, upper-contour strategy-proofness. Our main result is even though sd-strategy-proofness is weakened to upper-contour strategy-proofness, we end up with impossibility results.