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