Robustness of the incentive compatible combinatorial auction (original) (raw)
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Combinatorial auctions in the information age: An experimental study
2002
In private values settings, the Vickrey-Clarke-Groves (VCG) mechanism leads to efficient auction outcomes, while the theoretical properties of the Simultaneous Ascending (SA) auction are not well understood. This leads us to compare the properties of an SA and a VCG auction in an experimental setting with private values for multiple objects having complementarities. Statistically, we find little to distinguish the two auctions with both auction forms achieving more than 98% efficiency and extracting roughly 95% of the available surplus. Finally, in contrast to experimental results in single object VCG settings, the theoretical prediction of demand revelation in the multiple object VCG auction is largely supported in our experiments.
Pricing combinatorial auctions
European Journal of Operational Research, 2004
Single-item auctions have many desirable properties. Mechanisms exist to ensure optimality, incentive compatibility and market-clearing prices. When multiple items are offered through individual auctions, a bidder wanting a bundle of items faces an exposure problem if the bidder places a high value on a combination of goods but a low value on strict subsets of the desired collection. To remedy this, combinatorial auctions permit bids on bundles of goods. However, combinatorial auctions are hard to optimize and may not have incentive compatible mechanisms or market-clearing individual item prices. Several papers give approaches to provide incentive compatibility and imputed, individual prices. We find the relationships between these approaches and analyze their advantages and disadvantages.
Incentive compatible multi unit combinatorial auctions
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge - TARK '03, 2003
School of C o m p u t e r Science a n d Engineering, H e b r e w University, J e r u s a l e m 91904, Israel A b s t r a c t This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.
A Comparison of Multiple-Unit All-Pay and Winner-Pay Auctions Under Incomplete Information*
International Economic Review, 2002
This paper examines the properties of independent-private-value all-pay and winner-pay auctions when there are multiple units sold. We study bidding behavior, efficiency and revenue in a set of nine experimental sessions, each with six bidders. All-pay auctions were played in six of the sessions, three sessions with four units and three sessions with two units auctioned. A four-unit winner-pay auction was played in three of the sessions. Our data show that the all-pay auction and the winner-pay auction are empirically revenue equivalent and yield higher revenue than the risk neutral Bayesian equilibrium. Revenue is higher in the allpay auction when K=2 than when K=4, despite the fact that Bayesian equilibrium revenues are identical for the two cases. Our evidence also suggests that the winner-pay auction is more likely than the all-pay auction to lead to a Pareto-efficient allocation.
Proceedings of the 10th …, 2009
Restricting the preferences of the agents by assuming that their utility functions linearly depend on a payment allows for the positive results of the Vickrey auction and the Vickrey-Clarke-Groves mechanism. These results, however, are limited to settings where there is some commonly desired commodity or numeraire--money, shells, beads, etcetera--which is commensurable with utility. We propose a generalization of the Vickrey auction that does not assume that the agents' preferences are quasilinear, but nevertheless retains ...
Introduction to Combinatorial Auctions
Combinatorial Auctions, 2005
Combinatorial auctions are those auctions in which bidders can place bids on combinations of items, called "packages," rather than just individual items. The study of combinatorial auctions is inherently interdisciplinary. Combinatorial auctions are in the first place auctions, a topic extensively studied by economists. 1 Package bidding brings in operations research, especially techniques from combinatorial optimization and mathematical programming. Finally, computer science is concerned with the expressiveness of various bidding languages, and the algorithmic aspects of the combinatorial problem. The study of combinatorial auctions thus lies at the intersection of economics, operations research, and computer science. In this book, we look at combinatorial auctions from all three perspectives. Indeed, our contribution is to do so in an integrated and comprehensive way. The initial challenge in interdisciplinary research is defining a common language. We have made an effort to use terms consistently throughout the book, with the most common terms defined in the glossary. There are numerous examples of combinatorial auctions in practice. As is typical of many fields, practice precedes theory. Simple combinatorial auctions have been used for many decades in, for example, estate auctions. A common procedure is to auction the individual items, and then, at the end, to accept bids for packages of items. If a package bid exceeds the sum of the individual bids for the items in the package, then the items are sold as a package. In this book we consider a variety of much more general combinatorial auctions, but the key ingredient is the same as in this simple case: each bidder can submit bids on packages of items. 2 Recently, combinatorial auctions have been employed in a variety of industries. For example, they have been used for truckload transportation, bus routes, and industrial procurement, and have been proposed for airport arrival and departure slots, as well as for allocating radio spectrum for wireless communications services. Combinatorial auctions for radio spectrum have been conducted in both the United States and Nigeria. In each case, the compelling motivation for the use of a combinatorial auction is the presence of complementarities among the items which differ across bidders. For example, a trucker's cost of handling shipments in one lane depends on its loads in other lanes. Similarly, a mobile phone operator may value licenses in two adjacent cities more than the sum of the individual license values, since the operator's customers value roaming between cities.
Proceedings of The National Academy of Sciences, 2003
Combinatorial auctions allow for more expressive bidding in which participants can submit package bids with logical constraints that limit allowable outcomes. This type of auction can be useful when participants' values are complementary or when participants have production and financial constraints. However, combinatorial auctions are currently rare in practice. The main problems confronted in implementing these auctions are that they have computational uncertainty (i.e., there is no guarantee that the winning bids for such an auction can be found in a ''reasonable'' amount of time when the number of bidders and items becomes larger) and that the auction is cognitively complex and can lead participants to pursue perverse bidding strategies. This article describes a type of combinatorial auction that, during laboratory testing, eliminated these problems and produced extremely efficient outcomes.
Basic auction theory revisited
International Journal of Economic Theory, 2015
We revisit the benchmark model of auctions and consider a more general class of utility functions that allow for income effects. We assume that all individuals have the same utility function but have different incomes. Incomes are private information. We analyze first-price, secondprice, and all-pay auctions and show that non-quasilinearity changes many basic results of the benchmark model. While Vickrey's (1961) result on second-price auctions is very robust, revenue equivalence breaks down even with risk-neutral bidders, high enough incomes and identically and independently distributed types. In most cases, we find that all-pay auctions fetch the highest expected revenue.
An Experimental Investigation of a Hybrid Auction.¤
2002
In this paper we report the results of an experiment designed to examine the properties of a hybrid auction -a Dutch-Vickrey auction, that combines a sealed bid …rst-price auction with a sealed bid second-price auction. We developed an independent-private-values model that yielded various predictions in terms of equilibrium behavior and expected revenue. We then designed an experiment where individuals participate in a sequence of independent …rst-price auctions followed by a sequence of hybrid auctions. Several conclusions emerged from this experimental study. Firstly, ex-post e¢ciency was achieved overwhelmingly by the hybrid auctions. Secondly, although overbidding (with respect to the risk-neutral Bayesian Nash equilibrium) was a regular feature of participants' bidding behavior in the …rst-price auctions -as it is commonly reported in most experimental studies of …rst-price auctions -it was less frequent in the hybrid auctions. By calibrating the results to allow for risk-averse behavior we were able to account for a signi…cant part of the overbidding. Finally, ¤ We are thankful to the direct …nancial support provided by EPGE/FGV. Dutra also acknowledges the …nancial support from CNPq and Menezes acknowledges the …nancial support from CNPq and ARC (Grant no. A000000055). We thank Aloisio Araujo, John Asker, Tim Cason, Simon Grant and Sergio Werlang for useful comments.