Expected Outcomes and Manipulations in Online Fair Division

TL;DR

This paper analyzes the computational aspects of two online fair division mechanisms, LIKE and BALANCED LIKE, focusing on their outcomes, strategic behavior, and tractability.

Contribution

It provides a comparative study of the computational complexity of outcome analysis and strategic bidding in LIKE and BALANCED LIKE mechanisms.

Findings

LIKE outcomes are more computationally tractable than BALANCED LIKE.

Computing strategic bids in BALANCED LIKE is intractable in general.

LIKE is strategy-proof, unlike BALANCED LIKE.

Abstract

Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we consider what expected outcomes are possible, what outcomes are necessary, and how to compute their exact outcomes. In general, we show that such questions are more tractable to compute for LIKE than for BALANCED LIKE. As LIKE is strategy-proof but BALANCED LIKE is not, we also consider the computational problem of how, with BALANCED LIKE, an agent can compute a strategic bid to improve their outcome. We prove that this problem is intractable in general.