Designing Coalition-Proof Reverse Auctions over Continuous Goods

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

Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions

Motivated by the increasing use of auctions by government agencies, we consider the problem of fairly pricing public goods in a combinatorial auction. A well-known problem with the incentive-compatible Vickrey-Clarke-Groves (VCG) auction mechanism is that the resulting prices may not be in the core. Loosely speaking, this means the payments of the winners could be so low, that there are losing bidders who would have been willing to pay more than the payments of the winning bidders. Clearly, this ``unfair\u27\u27 outcome is unacceptable for a public-sector auction. Proxy-based combinatorial auctions, in which each bidder submits several package bids to a proxy, result in efficient outcomes and bidder-Pareto-optimal core-payments by winners, thus offering a viable practical alternative to address this problem. This paper confronts two critical issues facing the proxy-auction. First, motivated to minimize a bidder\u27s ability to benefit through strategic manipulation (through collusive agreement or unilateral action), we demonstrate the strength of a mechanism that minimizes total payments among all possible proxy auction outcomes, narrowing the previously broad solution concept. Secondly, we address the computational difficulties of achieving these outcomes with a constraint-generation approach, promising to broaden the range of applications for which the proxy-auction achieves a comfortably rapid solution

Parallelisation and application of AD3 as a method for solving large scale combinatorial auctions

Auctions, and combinatorial auctions (CAs), have been successfully employed to solve coordination problems in a wide range of application domains. However, the scale of CAs that can be optimally solved is small because of the complexity of the winner determination problem (WDP), namely of finding the bids that maximise the auctioneer’s revenue. A way of approximating the solution of a WDP is to solve its linear programming relaxation. The recently proposed Alternate Direction Dual Decomposition algorithm (AD3) has been shown to ef- ficiently solve large-scale LP relaxations. Hence, in this paper we show how to encode the WDP so that it can be approximated by means of AD3. Moreover, we present PAR-AD3, the first parallel implementation of AD3. PAR-AD3 shows to be up to 12.4 times faster than CPLEX in a single-thread execution, and up to 23 times faster than parallel CPLEX in an 8-core architecture. Therefore PAR- AD3 becomes the algorithm of choice to solve large-scale WDP LP relaxations for hard instances. Furthermore, PAR-AD3 has potential when considering large- scale coordination problems that must be solved as optimisation problems.Research supported by MICINN projects TIN2011-28689-C02-01, TIN2013-45732-C4-4-P and TIN2012-38876-C02-01Peer reviewe

Models for Budget Constrained Auctions: An Application to Sponsored Search & Other Auctions

The last decade has seen the emergence of auction mechanisms for pricing and allocating goods on the Internet. A successful application area for auctions has been sponsored search. Search firms like Google, Bing and Yahoo have shown stellar revenue growths due to their ability to run large number of auctions in a computationally efficient manner. The online advertisement market in the U.S. is estimated to be around $41 billion in 2010 and expected to grow to$50 billion by 2011 (http://www.marketingcharts.com/interactive/us-online-advertising-market-to-reach-50b-in-2011-3128/). The paid search component is estimated to account for nearly 50% of online advertising spend. This dissertation considers two problems in the sponsored search auction domain. In sponsored search, the search operator solves a multi-unit allocation and pricing problem with the specified bidder values and budgets. The advertisers, on the other hand, regularly solve a bid determination problem for the different keywords, given their budget and other business constraints. We develop a model for the auctioneer that allows the bidders to place differing bids for different advertisement slots for any keyword combination. Despite the increased complexity, our model is solved in polynomial time. Next, we develop a column-generation procedure for large advertisers to bid optimally in the sponsored search auctions. Our focus is on solving large-scale versions of the problem. Multi-unit auctions have also found a number of applications in other areas that include supply chain coordination, wireless spectrum allocation and transportation. Current research in the multi-unit auction domain ignores the budget constraint faced by participants. We address the computational issues faced by the auctioneer when dealing with budget constraints in a multi-unit auction. We propose an optimization model and solution approach to ensure that the allocation and prices are in the core. We develop an algorithm to determine an allocation and Walrasian equilibrium prices (when they exist) under additive bidder valuations where the auctioneer's goal is social welfare maximization and extend the approach to address general package auctions. We, also, demonstrate the applicability of the Benders decomposition technique to model and solve the revenue maximization problem from an auctioneer's standpoint

A Pareto-metaheuristic for a bi-objective winner determination problem in a combinatorial reverse auction

The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts comes up to a multi-criteria set covering problem. We are given a set B of bundle bids. A bundle bid b in B consists of a bidding carrier c_b, a bid price p_b, and a set tau_b of transport contracts which is a subset of the set T of tendered transport contracts. Additionally, the transport quality q_t,c_b is given which is expected to be realized when a transport contract t is executed by a carrier c_b. The task of the auctioneer is to find a set X of winning bids (X is subset of B), such that each transport contract is part of at least one winning bid, the total procurement costs are minimized, and the total transport quality is maximized. This article presents a metaheuristic approach for the 2WDP-SC which integrates the greedy randomized adaptive search procedure, large neighborhood search, and self-adaptive parameter setting in order to find a competitive set of non-dominated solutions. The procedure outperforms existing heuristics. Computational experiments performed on a set of benchmark instances show that, for small instances, the presented procedure is the sole approach that succeeds to find all Pareto-optimal solutions. For each of the large benchmark instances, according to common multi-criteria quality indicators of the literature, it attains new best-known solution sets.Pareto optimization; multi-criteria winner determination; combinatorial auction; GRASP; LNS