Marginal Mechanisms For Balanced Exchange

TL;DR

This paper analyzes mechanisms for balanced exchange problems with indivisible objects, focusing on marginal preferences, and characterizes domains where efficient, rational, and strategy-proof mechanisms can be designed.

Contribution

It identifies the maximal domains of marginal preferences allowing for unambiguous, efficient, and strategy-proof mechanisms, introducing a family of gradual-revelation mechanisms.

Findings

The maximal domain for unambiguous efficiency and rationality is trichotomous with no endowed objects in the bottom tier.

The maximal domain for strategy-proofness is strongly trichotomous, excluding endowed objects from the middle tier.

A serial dictatorship mechanism achieves the three desiderata on the strongly trichotomous domain, with variants providing better incentives.

Abstract

We study balanced exchange problems in which agents with responsive preferences are endowed with multiple indivisible objects and can trade without transfers (e.g. shift exchange, time-banking). Eliciting full preferences over bundles is infeasible, so mechanisms often 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 containing no endowed objects. We also consider incentives for truthful preference revelation. The maximal domain for which an efficient, individually rational, and strategy-proof mechanism exists is strongly trichotomous: agents rank objects in three tiers, with the bottom tier containing no endowed objects and the middle tier containing no non-endowed objects. The canonical marginal mechanism achieving our three desiderata on that domain is a serial dictatorship over individually rational allocations. When employed on the larger trichotomous domain, this mechanism still admits a weakly dominant strategy: reveal the top tier truthfully and omit non-endowed objects from the middle tier. We propose a family of gradual-revelation mechanisms that are also unambiguously efficient and individually rational on the trichotomous domain while providing better incentives for truthful revelation across all three tiers.