Strategyproof and Consistent Rules for Bipartite Flow Problems

TL;DR

This paper introduces the edge fair mechanism for bipartite flow problems, achieving both consistency and group strategyproofness, and explores the fundamental trade-offs between fairness and consistency in such allocation models.

Contribution

It proposes a new mechanism that combines consistency with group strategyproofness and generalizes existing proofs to broader classes of mechanisms.

Findings

The edge fair mechanism is both consistent and group strategyproof.

Consistency conflicts with certain fairness notions like Lorenz Dominance and No-Envy.

The study extends to transshipment models with strategic agents on links.

Abstract

We continue the study of Bochet et al. and Moulin and Sethuraman on fair allocation in bipartite networks. In these models, there is a moneyless market, in which a non-storable, homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. While the egalitarian rule of Bochet et al. satisfies pareto optimality, no envy and strategyproof, it is not consistent. On the other hand, the work of Moulin and Sethuraman is related to consistent allocations and rules that are extensions of the uniform rule. We bridge the two streams of work by introducing the edge fair mechanism which is both consistent and groupstrategyproof. On the way, we explore the "price of consistency" i.e. how the notion of consistency is fundamentally incompatible with certain notions of fairness like Lorenz Dominance and No-Envy. The current work also introduces the idea of strong invariance as desideratum for groupstrategyproofness and generalizes the proof of Chandramouli and Sethuraman to a more broader class of mechanisms. Finally, we conclude with the study of the edge fair mechanism in a transshipment model where the strategic agents are on the links connecting different supply/demand locations.