Truthful Allocation Mechanisms Without Payments: Characterization and Implications on Fairness

TL;DR

This paper characterizes truthful, payment-free allocation mechanisms for indivisible items with two players, revealing a structure that combines selection and exchange components, and explores fairness guarantees and their bounds.

Contribution

It provides a complete characterization of truthful mechanisms without payments for two players, unveiling their underlying structure and implications for fairness.

Findings

Mechanisms decompose into selection and exchange parts.

Tight bounds established for fairness guarantees.

Settles open problems on fairness approximability.

Abstract

We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on the case of two players with additive valuation functions and our purpose is twofold. First, our main result provides a complete characterization of truthful mechanisms that allocate all the items to the players. Our characterization reveals an interesting structure underlying all truthful mechanisms, showing that they can be decomposed into two components: a selection part where players pick their best subset among prespecified choices determined by the mechanism, and an exchange part where players are offered the chance to exchange certain subsets if it is favorable to do so. In the remaining paper, we apply our main result and derive several consequences on the design of mechanisms with fairness guarantees. We consider various notions of fairness, (indicatively, maximin share guarantees and envy-freeness up to one item) and provide tight bounds for their approximability. Our work settles some of the open problems in this agenda, and we conclude by discussing possible extensions to more players.