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20
Revenue monotonicity in combinatorial auctions
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2007
"... Intuitively, one might expect that a seller’s revenue from an auction weakly increases as the number of bidders grows, as this increases competition. However, it is known that for combinatorial auctions that use the VCG mechanism, a seller can sometimes increase revenue by dropping bidders. In this ..."
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Cited by 20 (3 self)
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Intuitively, one might expect that a seller’s revenue from an auction weakly increases as the number of bidders grows, as this increases competition. However, it is known that for combinatorial auctions that use the VCG mechanism, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this problem can occur under other dominantstrategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity ” are not limited to mechanisms that achieve efficient allocations. Instead, they can occur under any dominantstrategy direct mechanism that sets prices using critical values, and that always chooses an allocation that cannot be augmented to make some bidder better off, while making none worse off.
A Theory of Expressiveness in Mechanisms
, 2007
"... A key trend in the world—especially in electronic commerce—is a demand for higher levels of expressiveness in the mechanisms that mediate interactions, such as the allocation of resources, matching of peers, and elicitation of opinions from large and diverse communities. Intuitively, one would think ..."
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Cited by 15 (9 self)
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A key trend in the world—especially in electronic commerce—is a demand for higher levels of expressiveness in the mechanisms that mediate interactions, such as the allocation of resources, matching of peers, and elicitation of opinions from large and diverse communities. Intuitively, one would think that this increase in expressiveness would lead to more efficient mechanisms (e.g., due to better matching of supply and demand). However, until now we have lacked a general way of characterizing the expressiveness of these mechanisms, analyzing how it impacts the actions taken by rational agents—and ultimately the outcome of the mechanism. In this technical report we introduce a general model of expressiveness for mechanisms. Our model is based on a new measure which we refer to as the maximum impact dimension. The measure captures the number of different ways that an agent can impact the outcome of a mechanism. We proceed to uncover a fundamental connection between this measure and the concept of shattering from computational learning theory. We also provide a way to determine an upper bound on the expected efficiency of any mechanism under its most efficient Nash equilibrium which, remarkably, depends only on the mechanism’s expressiveness. We show that for any setting and any prior over agent preferences, the
Position auctions with bidderspecific minimum
 In Internet and Network Economics, LNCS 5385
, 2008
"... Position auctions such as the Generalized Second Price (GSP) are commonly used for sponsored search, e.g., by Yahoo! and Google. We now have an understanding of the equilibria of these auctions, via gametheoretic concepts like Generalized English Auctions and the “locally envyfree ” property, as w ..."
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Cited by 7 (1 self)
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Position auctions such as the Generalized Second Price (GSP) are commonly used for sponsored search, e.g., by Yahoo! and Google. We now have an understanding of the equilibria of these auctions, via gametheoretic concepts like Generalized English Auctions and the “locally envyfree ” property, as well as through a relationship to the wellknown, truthful VickreyClarkeGroves (VCG) mechanism. In practice, however, position auctions are implemented with additional constraints, in particular, bidderspecific minimum prices. Such minimum prices are used to control the quality of the ads that appear on the page. We study the effect of bidderspecific minimum prices in position auctions. Naïvely enforcing minimum prices in the VCG mechanism breaks the truthfulness of the auction; we describe two variants of VCG for which revealing the truth is a dominant strategy. The implications of bidderspecific minimum prices are more intricate for the GSP auction. Some properties proved for standard GSP no longer hold in this setting. For example, we show that the GSP allocation is now not always efficient (in terms of advertiser value). Also, the property of“envylocality”enjoyed by GSP—which is essential in the prior analysis of strategies and equilibria— no longer holds. Our main result is to show that despite losing envy locality, GSP with bidderspecific minimum prices still has an envyfree equilibrium. 1.
Comparing multiagent systems research in combinatorial auctions and voting
 Annals of Mathematics and Artificial Intelligence
"... In a combinatorial auction, a set of items is for sale, and agents can bid on subsets of these items. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this p ..."
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Cited by 4 (2 self)
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In a combinatorial auction, a set of items is for sale, and agents can bid on subsets of these items. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this paper is to give a convenient sidebyside comparison that will clarify the relation between the domains, and serve as a guide to future research. 1
Envy Quotes and the Iterated CoreSelecting Combinatorial Auction ∗
"... Using a model of agent behavior based around envyreducing strategies, we describe an iterated combinatorial auction in which the allocation and prices converge to a solution in the core of the agents ’ true valuations. In each round of the iterative auction mechanism, agents act on envy quotes prod ..."
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Cited by 4 (0 self)
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Using a model of agent behavior based around envyreducing strategies, we describe an iterated combinatorial auction in which the allocation and prices converge to a solution in the core of the agents ’ true valuations. In each round of the iterative auction mechanism, agents act on envy quotes produced by the mechanism: hints that suggest the prices of the bundles they are interested in. We describe optimal methods of generating envy quotes for various coreselecting mechanisms. Prior work on coreselecting combinatorial auctions has required agents to have perfect information about every agent’s valuations to achieve a solution in the core. In contrast, here a core solution is reached even in the private information setting.
Analysis and Optimization of Multidimensional Percentile Mechanisms
"... We consider the mechanism design problem for agents with singlepeaked preferences over multidimensional domains when multiple alternatives can be chosen. Facility location and committee selection are classic embodiments of this problem. We propose a class of percentile mechanisms, a form of genera ..."
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Cited by 2 (2 self)
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We consider the mechanism design problem for agents with singlepeaked preferences over multidimensional domains when multiple alternatives can be chosen. Facility location and committee selection are classic embodiments of this problem. We propose a class of percentile mechanisms, a form of generalized median mechanisms, that are (group) strategyproof, and derive worstcase approximation ratios for social cost and maximum load for L1 and L2 cost models. More importantly, we propose a samplebased framework for optimizing the choice of percentiles relative to any prior distribution over preferences, while maintaining strategyproofness. Our empirical investigations, using social cost and maximum load as objectives, demonstrate the viability of this approach and the value of such optimized mechanisms visàvis mechanisms derived through worstcase analysis. 1
Revenue Monotonicity in Deterministic, DominantStrategy Combinatorial Auctions
, 2009
"... In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic dominantstrategy combinatorial auction mechanisms. Our main result is that su ..."
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Cited by 2 (0 self)
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In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic dominantstrategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity” can occur under any such mechanism that is weakly maximal—meaning roughly that it chooses allocations that cannot be augmented to cause a losing bidder to win without hurting winning bidders—and that allows bidders to express arbitrary singleminded preferences. We also give a set of other impossibility results as corollaries, concerning revenue when the set of goods changes, falsenameproofness, and the core.
Approximating Optimal Combinatorial Auctions for Complements Using Restricted Welfare Maximization ∗
"... The VCG mechanism is the gold standard for combinatorial auctions (CAs), and it maximizes social welfare. In contrast, the revenuemaximizing (aka optimal) CA is unknown, and designing one is NPhard. Therefore, research on optimal CAs has progressed into special settings. Notably, Levin [1997] deri ..."
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Cited by 2 (2 self)
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The VCG mechanism is the gold standard for combinatorial auctions (CAs), and it maximizes social welfare. In contrast, the revenuemaximizing (aka optimal) CA is unknown, and designing one is NPhard. Therefore, research on optimal CAs has progressed into special settings. Notably, Levin [1997] derived the optimal CA for complements when each agent’s private type is onedimensional. (This does not fall inside the wellstudied “singleparameter environment”.) We introduce a new research avenue for increasing revenue where we poke holes in the allocation space—based on the bids—and then use a welfaremaximizing allocation rule within the remaining allocation set. In this paper, the first step down this avenue, we introduce a new form of “reserve pricing ” into CAs. We show that Levin’s optimal revenue can be 2approximated by using “monopoly reserve prices ” to curtail the allocation set, followed by welfaremaximizing allocation and Levin’s payment rule. A key lemma of potential independent interest is that the expected revenue from any truthful allocationmonotonic mechanism equals the expected virtual valuation; this generalizes Myerson’s lemma [1981] from the singleparameter environment. Our mechanism is close to the gold standard and thus easier to adopt than Levin’s. It also requires less information about the prior over the bidders ’ types, and is always more efficient. Finally, we show that the optimal revenue can be 6approximated even if the “reserve pricing ” is required to be symmetric across bidders. 1
Auction protocols
"... The word “auction ” generally refers to a mechanism for allocating one or more resources to one or more parties (or bidders). Generally, once the allocation is determined, some amount of money changes hands; the precise monetary transfers are determined by the auction process. While in some auction ..."
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Cited by 1 (1 self)
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The word “auction ” generally refers to a mechanism for allocating one or more resources to one or more parties (or bidders). Generally, once the allocation is determined, some amount of money changes hands; the precise monetary transfers are determined by the auction process. While in some auction protocols, such as the English auction, bidders repeatedly increase their bids in an attempt to outbid each other, this is not an essential component of an auction. There are many other auction protocols, and we will study some of them in this chapter. Auctions have traditionally been studied mostly by economists. In recent years, computer scientists have also become interested in auctions, for a variety of reasons. Auctions can be useful for allocating various computing resources across users. In artificial intelligence, they can be used to allocate resources and tasks across multiple artificially intelligent “agents. ” Auctions are also important in electronic commerce: there are of course several wellknown auction websites, but additionally, search engines use auctions to sell advertising space on their results pages. Finally, increased computing power and improved algorithms have made new types of auctions possible—most notably combinatorial auctions, in which
A New Analysis of Revenue in the Combinatorial and Simultaneous Auction
, 2009
"... We prove that in many cases, a firstprice sealedbid combinatorial auction gives higher expected revenue than a sealedbid simultaneous auction. This is the first theoretical evidence that combinatorial auctions indeed generate higher revenue, which has been a common belief for decades. We use a mo ..."
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We prove that in many cases, a firstprice sealedbid combinatorial auction gives higher expected revenue than a sealedbid simultaneous auction. This is the first theoretical evidence that combinatorial auctions indeed generate higher revenue, which has been a common belief for decades. We use a model with many bidders and items, where bidders are of two types: (i) singlebidders interested in only one item and (ii) synergybidders, each interested in one random combination of items. We provide an upper bound on the expected revenue for simultaneous auctions and a lower bound on combinatorial auctions. Our bounds are parameterized on the number of bidders and items, combination size, and synergy. We derive an asymptotic result, proving that as the number of bidders approach infinity, expected revenue of the combinatorial auction will be higher than that of the simultaneous auction. We also provide concrete examples where the combinatorial auction is revenuesuperior. 1