Designing Coalition-Proof Reverse Auctions over Continuous Goods

TL;DR

This paper develops coalition-proof reverse auction mechanisms for continuous goods, identifying conditions for coalition resistance and proposing computationally efficient payment methods, validated through electricity market case studies.

Contribution

It introduces new coalition-proof payment rules for complex reverse auctions and provides efficient algorithms for their computation.

Findings

Coalition-proof outcomes are achieved with convex bids and polymatroid constraints under VCG.

Relaxed conditions allow coalition-proof mechanisms without bid or constraint restrictions.

Two efficient algorithms are proposed for computing payments in large-scale auctions.

Abstract

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the incentive-compatible Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of a polymatroid-type. These conditions, however, do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof without any extra conditions on the submitted bids and the constraint sets. Since calculating the payments directly for these mechanisms is computationally difficult for auctions involving many participants, we present two computationally efficient methods. Our results are verified with several case studies based on electricity market data.