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

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

Core-competitive Auctions

One of the major drawbacks of the celebrated VCG auction is its low (or zero) revenue even when the agents have high value for the goods and a {\em competitive} outcome could have generated a significant revenue. A competitive outcome is one for which it is impossible for the seller and a subset of buyers to `block' the auction by defecting and negotiating an outcome with higher payoffs for themselves. This corresponds to the well-known concept of {\em core} in cooperative game theory. In particular, VCG revenue is known to be not competitive when the goods being sold have complementarities. A bottleneck here is an impossibility result showing that there is no auction that simultaneously achieves competitive prices (a core outcome) and incentive-compatibility. In this paper we try to overcome the above impossibility result by asking the following natural question: is it possible to design an incentive-compatible auction whose revenue is comparable (even if less) to a competitive outcome? Towards this, we define a notion of {\em core-competitive} auctions. We say that an incentive-compatible auction is $\alpha$-core-competitive if its revenue is at least $1/\alpha$ fraction of the minimum revenue of a core-outcome. We study the Text-and-Image setting. In this setting, there is an ad slot which can be filled with either a single image ad or $k$ text ads. We design an $O(\ln \ln k)$ core-competitive randomized auction and an $O(\sqrt{\ln(k)})$ competitive deterministic auction for the Text-and-Image setting. We also show that both factors are tight

Core-Selecting Auctions for Dynamically Allocating Heterogeneous VMs in Cloud Computing

In a cloud market, the cloud provider provisions heterogeneous virtual machine (VM) instances from its resource pool, for allocation to cloud users. Auction-based allocations are efficient in assigning VMs to users who value them the most. Existing auction design often overlooks the heterogeneity of VMs, and does not consider dynamic, demand-driven VM provisioning. Moreover, the classic VCG auction leads to unsatisfactory seller revenues and vulnerability to a strategic bidding behavior known as shill bidding. This work presents a new type of core-selecting VM auctions, which are combinatorial auctions that always select bidder charges from the core of the price vector space, with guaranteed economic efficiency under truthful bidding. These auctions represent a comprehensive three-phase mechanism that instructs the cloud provider to judiciously assemble, allocate, and price VM bundles. They are proof against shills, can improve seller revenue over existing auction mechanisms, and can be tailored to maximize truthfulness.published_or_final_versio

Approximate Strategyproofness

The standard approach of mechanism design theory insists on equilibrium behavior by participants. This assumption is captured by imposing incentive constraints on the design space. But in bridging from theory to practice, it often becomes necessary to relax incentive constraints in order to allow tradeoffs with other desirable properties. This article surveys a number of different options that can be adopted in relaxing incentive constraints, providing a current view of the state-of-the-art.Engineering and Applied Science

Quadratic Core-Selecting Payment Rules for Combinatorial Auctions

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a series of economically meaningful and equitable penalties. Furthermore, we discuss the benefits of this combinatorial auction, explore the use of alternative reserve pricing approaches in this context, and indicate the results of several hundred computational runs using CATS data.Auctions, spectrum auctions, market design, package auction, clock auction, combinatorial auction