The Machiavellian frontier of stable mechanisms
Abstract
The impossibility theorem in Roth (1982) states that no stable mechanism satisfies strategy-proofness. This paper explores the Machiavellian frontier of stable mechanisms by weakening strategy-proofness. For a fixed mechanism and a true preference profile , a (,)-boost mispresentation of agent i is a preference of i that is obtained by (i) raising the ranking of the truth-telling assignment i(), and (ii) keeping rankings unchanged above the new position of this truth-telling assignment. We require a matching mechanism neither punish nor reward any such misrepresentation, and define such axiom as -boost-invariance. This is strictly weaker than requiring strategy-proofness. We show that no stable mechanism satisfies -boost-invariance. Our negative result strengthens the Roth Impossibility Theorem.
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