Groupstrategyproofness of the Egalitarian Mechanism for Constrained Rationing Problems

TL;DR

This paper proves that the egalitarian mechanism for constrained rationing is peak group strategyproof, meaning no coalition of agents can benefit from misreporting, and simplifies previous proofs of strategyproofness.

Contribution

It establishes the peak group strategyproofness of the egalitarian mechanism and extends this property to coalitions of suppliers and demanders, simplifying earlier proofs.

Findings

Egalitarian mechanism is peak group strategyproof.

Coalitions of suppliers or demanders cannot manipulate the mechanism.

Megiddo's algorithm for lexicographically optimal flow is group strategyproof.

Abstract

The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is, in fact, peak group strategyproof : no coalition of agents can (weakly) benefit from jointly misreporting their peaks. Furthermore, we show that the egalitarian mechanism cannot be manipulated by any coalition of suppliers (or any coalition of demanders) in the model where both the suppliers and demanders are agents. Our proofs shed light on the structure of the two models and simpify some of the earlier proofs of strategyproofness in the earlier papers. An implication of our results is that the well known algorithm of Megiddo to compute a lexicographically optimal flow in a network is group strategyproof with respect to the source capacities (or sink capacities).