1776687
An Approach to VCG-like Approximate Allocation and Pricing for Large-scale Multi-unit Combinatorial Auctions
A multi-unit combinatorial auction is a combinatorial auction that has some items that can be seen as in- distinguishable. Although the mechanism can be applied to dynamic electricity auctions and various purposes, it is difficult to apply to large-scale auction problems due to its computational intractability. In this paper, I present an idea and an analysis about an approximate allocation and pricing algorithm that is capable of handling multi-unit auctions. The analysis shows that the algorithm effectively produces approximation allocations that are necessary in pricing. Furthermore, the algorithm can be seen as an approximation of VCG (Vickrey-Clarke-Groves) mechanism satisfying budget balance condition and bidders' individual rationality without having unrealistic assumptions on bidders' be- haviors. I show that the proposed allocation algorithm successfully produced good allocations for those problems that could not be easily solved by ordinary LP solvers due to hard time constraints.
8139508
CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions
Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is \scr{N}\scr{P}-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster---especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem---the run-time distribution does not have a heavy tail.
153547379
Selling Spectrum Rights
The design of the FCC spectrum-license auction is a case study in the application of economic theory. Auction theory helped address policy questions such as: Should an open auction or a sealed-bid auction be used? Should the licenses be auctioned sequentially or simultaneously? Should the government allow bids for combinations of licenses, or should it accept only single-license bids? How should the auction be structured to promote the interests of minority-owned and other designated firms? Should the government impose royalties or reserve prices? How much should the bidders be informed about their competition?
5529095
Computationally Feasible VCG Mechanisms
A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG (Vickrey, Clarke, Groves). When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are, therefore, computationally infeasible. However, if the optimal outcome is replaced by the results of a sub-optimal algorithm, the resulting mechanism (termed VCG-based) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield non-truthful VCG-based mechanisms. We generalize these results for affine maximizers. 
 
The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCG-based mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm's output. We provide a strong rationale for truth-telling behavior. Our method satisfies individual rationality as well.
7147920
Distributed implementations of Vickrey-Clarke-Groves mechanisms
Mechanism design (MD) provides a useful method to implement outcomes with desirable properties in systems with self-interested computational agents. One drawback, however, is that computation is implicitly centralized in MD theory, with a central planner taking all decisions.We consider distributed implementations, in which the outcome is determined by the self-interested agents themselves. Clearly this introduces new opportunities for manipulation.We propose a number of principles to guide the distribution of computation, focusing in particular on Vickrey-Clarke-Groves mechanisms for implementing outcomes that maximize total value across agents. Our solutions bring the complete implementation into an ex post Nash equilibrium.
6114062
Towards a universal test suite for combinatorial auction algorithms
General combinatorial auctions—auctions in which bidders place unrestricted bids for bundles of goods—are the subject of increasing study. Much of this work has focused on algorithms for finding an optimal or approximately optimal set of winning bids. Comparatively little attention has been paid to methodical evaluation and comparison of these algorithms. In particular, there has not been a systematic discussion of appropriate data sets that can serve as universally accepted and well motivated benchmarks. In this paper we present a suite of distribution families for generating realistic, economically motivated combinatorial bids in five broad real-world domains. We hope that this work will yield many comments, criticisms and extensions, bringing the community closer to a universal combinatorial auction test suite.
1415898
Toward Combinatorial Auction-based Better Electric Power Allocation on Sustainable Electric Power Systems
Multi-unit combinatorial auction is a combinatorial auction that has some items that can bee seen as indistinguishable. Some approximation mechanisms have been proposed to be applied for a large-scale auction problem regardless of its computational intractability. Although theoretically such mechanisms could be applied for dynamic electricity auctions, there is little empirical analysis about how such a fast approximation mechanism can be applied to the actual electric power allocation problem when we consider the situation that there are sustainable electric power sources and the consumers have preferences for them. In this paper, we present a preliminary analysis about applying a fast approximation mechanism for multi-unit combinatorial auctions to an electric power allocation problem when it includes sustainable power sources. Also in this paper we discuss how such a mechanism can be implemented in a practical way.
13941986
An Approach to Sustainable Electric Power Allocation Using a Multi-round Multi-unit Combinatorial Auction
In this paper, we present a preliminary idea about applying multi-unit combinatorial auctions to an electric power allocation problem when it includes sustainable power sources and it considers guaranteeing stable continuous use of the supplied power. Multi-unit combinatorial auction is a combinatorial auction that has some items that can be seen as indistinguishable. Theoretically, such mechanisms could be applied for dynamic electricity auctions. We try to illustrate how such a mechanism can be applied to the actual electric power allocation problem when we consider the situation that there are sustainable electric power sources and guaranteeing stable continuous use of them. An approximation mechanism has been applied for a large-scale auction problem to overcome its computational intractability.
2577743
An efficient approximate allocation algorithm for combinatorial auctions
We propose a heuristic for allocation in combinatorial auctions. We first run an approximation algorithm on the linear programming relaxation of the combinatorial auction. We then run a sequence of greedy algorithms, starting with the order on the bids determined by the approximate linear program and continuing in a hill-climbing fashion using local improvements in the order of bids. We have implemented the algorithm and have tested it on the complete corpus of instances provided by Vohra and de Vries as well as on instances drawn from the distributions of Leyton-Brown, Pearson, and Shoham. Our algorithm typically runs two to three orders of magnitude faster than the reported running times of Vohra and de Vries, while achieving an average approximation error of less than 1%. This algorithm can provide, in less than a minute of CPU time, excellent solutions for problems with over 1000 items and 10,000 bids. We thus believe that combinatorial auctions for most purposes face no practical computational hurdles.
15889327
Towards Better Approximation of Winner Determination for Combinatorial Auctions with Large Number of Bids
We propose new approximate algorithms for combinatorial auctions with massively large number of (more than 100,000) bids. In this paper, we focus on a more practical approximated algorithm in the context of revenue maximization. We propose a hill-climbing greedy algorithm, a SA-like random search algorithm, and their enhancement for searching multiple key parameter values. The experimental results demonstrate that our algorithms perform approximately 0.997 optimality compared with the optimal solutions and better than previously presented approximated algorithms. We also demonstrate that our algorithms are a kind of anytime algorithm that bring better results in shorter computational time that can be applied to large and dynamic electronic markets.
122971274
Periodical Resource Allocation Using Approximated Combinatorial Auctions
Combinatorial auction, one of most popular market mechanisms, is well-known mechanism for effective resource allocation to self-interested agents. In real scenarios, since the auction mechanism has to clear the market very frequently, actually there is not enough time to compute exact optimal winners. In this paper, we show that some approximation algorithms provide sufficient quality of winners for auctions that have large number of bids but have hard time constraints. Furthermore, we compare and discuss about desirable properties of such approximation algorithms to be embedded in application systems.
20000085
Toward a Large Scale E-Market: A Greedy and Local Search Based Winner Determination
Combinatorial auction is one of the most popular market mechanisms and it has a huge effect on electronic markets and political strategies. On large scale e-markets, we need a good approximation algorithm for winner determination that is robust for changing the distribution and the number of bids in an auction. We proposed approximate algorithms for combinatorial auctions with massively large number of (more than 100,000) bids. In this paper, we show the robustness of our winner determination algorithms for combinatorial auctions with large number of bids. Experimental results demonstrate that our proposed algorithms are robust on changing the distribution and the number of bids in an auction. Finally, we shortly describe a theoretical limitation about our algorithms that concerns with giving truthfulness of the auction mechanism.
7580259
An experimental analysis of biased parallel greedy approximation for combinatorial auctions
Considering emerging demands for auction based efficient resource allocations, the ability to complete an auction within a fine-grained time period without loss of allocation efficiency is in strong demand. Recently, an algorithm has been proposed to obtain near-optimal solutions for winner determination problem on combinatorial auctions within a very short computation time. However, it is demanded to analyse and clarify the main factor of such an excellent performance of the algorithm. Also, for practical use, there are demands to clarify the actual implementation-level performance of the algorithm compared to major commercial-level generic problem solvers. In this paper, we show an analysis about performance issues of biased parallel greedy updating approach in various experimental settings. Furthermore, we show that the algorithm has a certain advantage to solve a kind of large-size high-complexity problems when it is compared to a latest commercial-level implementation of generic LP solver through various experiments.
17391315
Toward a VCG-Like Approximate Mechanism for Large-Scale Multi-unit Combinatorial Auctions
Multi-unit combinatorial auction is a combinatorial auction that has some items that can bee seen as indistinguishable. Although the mechanism can be applied for dynamic electricity auctions and various purposes, it is difficult to be applied for large-scale auction problems due to its computational intractability. In this paper, I introduce a mechanism that employs an approximate allocation and pricing algorithm that is capable to handle multi-unit auctions. The algorithm effectively produce approximation allocations that are necessary in pricing and it behaves as an approximation of VCG(Vickrey-Clarke-Groves) mechanism satisfying budget balance condition and bidders' individual rationality without having single-minded bidders assumption. I show that the proposed allocation algorithm successfully produced good allocations for the problems that cannot be easily solved by ordinary LP solvers due to hard time constraints.
1207736
An Algorithm for Multi-Unit Combinatorial Auctions
We present a novel algorithm for computing the optimal winning bids in a combinatorial auction (CA), that is, an auction in which bidders bid for bundles of goods. All previously published algorithms are limited to single-unit CAs, already a hard computational problem. In contrast, here we address the more general problem in which each good may have multiple units, and each bid speci€es an unrestricted number of units desired from each good. We prove the correctness of our branch-and-bound algorithm, which incorporates a specialized dynamic programming procedure. We then provide very encouraging initial experimental results from an implemented version of the algorithm.
3204615
Optimal solutions for multi-unit combinatorial auctions: branch and bound heuristics
Finding optimal solutions for multi-unit combinatorial auctions is a hard problem and finding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from above the value of the best allocation and a good criterion to decide which bids are to be tried first. Different methods for efficiently bounding from above the value of the best allocation are considered. Theoretical original results characterize the best approximation ratio and the ordering criterion that provides it. We suggest to use this criterion.
2916748
Truth revelation in rapid, approximately efficient combinatorial auctions
Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms - in particular, their truth revelation properties - assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method, which has empirically been shown to perform well. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying sufficient conditions for a combinatorial auction to be truth-revealing, conditions which have applicability beyond the specific auction studied here.
5732121
Solving Combinatorial Auctions Using Stochastic Local Search
Combinatorial auctions (CAs) have emerged as an important model in economics and show promise as a useful tool for tackling resource allocation in AI. Unfortunately, winner determination for CAs is NP-hard and recent algorithms have difficulty with problems involving goods and bids beyond the hundreds. We apply a new stochastic local search algorithm, Casanova, to this problem, and demonstrate that it finds high quality (even optimal) solutions much faster than recently proposed methods (up to several orders of magnitude), particularly for large problems. We also propose a logical language for naturally expressing combinatorial bids in which a single logical bid corresponds to a large (often exponential) number of explicit bids. We show that Casanova performs much better than systematic methods on such problems.
9738574
Truthful approximation mechanisms for restricted combinatorial auctions
When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.
2414504
Monotone branch-and-bound search for restricted combinatorial auctions
Faced with an intractable optimization problem, a common approach to computational mechanism design seeks a polynomial time approximation algorithm with an approximation guarantee. Rather than adopt this worst-case viewpoint, we introduce a new paradigm that seeks to obtain good performance on typical instances through a modification to the branch-and-bound search paradigm. Incentive compatibility in single-dimensional domains requires that an outcome improves monotonically for an agent as the agent's reported value increases. We obtain a monotone search algorithm by coupling an explicit sensitivity analysis on the decisions made during search with a correction to the outcome to ensure monotonicity. Extensive computational experiments on single-minded combinatorial auctions show better welfare performance than that available from existing approximation algorithms.