Randomized Strategyproof Mechanisms with Best of Both Worlds Fairness and Efficiency

TL;DR

This paper introduces randomized mechanisms for allocating indivisible items among agents, achieving strategyproofness, fairness, and efficiency simultaneously, overcoming deterministic impossibility results.

Contribution

It presents novel randomized mechanisms that ensure strategyproofness and fairness in both chores and mixed item settings, especially for two agents.

Findings

Deterministic strategyproof, fair, and efficient mechanisms do not exist for chores.

Randomized mechanisms can achieve strategyproofness and fairness in expectation.

Mechanisms are effective for two agents with mixed items.

Abstract

We study the problem of mechanism design for allocating a set of indivisible items among agents with private preferences on items. We are interested in such a mechanism that is strategyproof (where agents' best strategy is to report their true preferences) and is expected to ensure fairness and efficiency to a certain degree. We first present an impossibility result that a deterministic mechanism does not exist that is strategyproof, fair and efficient for allocating indivisible chores. We then utilize randomness to overcome the strong impossibility. For allocating indivisible chores, we propose a randomized mechanism that is strategyproof in expectation as well as ex-ante and ex-post (best of both worlds) fair and efficient. For allocating mixed items, where an item can be a good (i.e., with a positive utility) for one agent but a chore (i.e., a with negative utility) for another, we propose a randomized mechanism that is strategyproof in expectation with best of both worlds fairness and efficiency when there are two agents.