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