Multidimensional bargaining and posted prices

Abstract

A seller and a buyer bargain over the quantities and prices of multiple goods. Both agents have private information about their preferences. Utility is quasilinear in money. We show that a deterministic mechanism satisfies (i) dominant-strategy incentive compatibility, (ii) ex-post individual rationality and (iii) ex-post budget balance if and only if it is a posted-price mechanism. A similar, more general result holds if (iii) is replaced by ex-post collusion-proofness and a no-free lunch condition. We provide a unified proof of both findings via the property of non-bossiness.