Marginal Mechanisms for Balanced Exchange
Paper joint with Vikram Manjunath
Abstract:
We study balanced exchange problems in which agents with responsive preferences are initially endowed with multiple indivisible objects and can trade without transfers, as in shift exchange or time-banking. In many such settings, eliciting or processing full preferences over bundles is infeasible. Instead, mechanisms rely solely on marginal preferences, that is, rankings of individual objects.
We characterize when eliciting only marginal preferences is enough to unambiguously identify allocations that are efficient and individually rational in the sense that these properties hold with respect to any responsive preferences consistent with the elicited marginals. We parameterize domains of marginal preferences by which indifference classes can contain endowed and non-endowed objects. We show that the essentially unique maximal domain for which an unambiguously efficient and unambiguously individually rational marginal mechanism exists is trichotomous: Agents rank objects in three tiers, with the bottom tier not containing any endowed objects.
We also consider agents’ incentives for truthful preference revelation. The maximal domain for which an efficient, individually rational, and strategy-proof mechanism, marginal or not, exists is strongly trichotomous: Agents rank objects in three tiers, with the bottom tier not containing any endowed objects and the middle tier not containing any non-endowed objects. The canonical marginal mechanism that unambiguously achieves our three desiderata on that domain is a serial dictatorship over the set of individually rational allocations. Interestingly, when employed on the larger trichotomous domain, this serial dictatorship mechanism still has a weakly dominant strategy: Reveal the top preference tier truthfully and do not reveal any non-endowed objects in the middle tier. We propose a new family of gradual-revelation mechanisms that are also unambiguously efficient and unambiguously individually rational on the trichotomous domain, while providing “better” incentives for the truthful revelation of all three preference tiers.