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13
Simultaneous Auctions are (almost) Efficient
, 2012
"... Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, base ..."
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Cited by 21 (5 self)
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Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. Such procedures occur in practice (e.g. eBay) but are not truthful. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first and secondprice auctions when bidders have complementfree (a.k.a. subadditive) valuations. We show that the expected social welfare of any BNE is at least 1 2 of the optimal social welfare in the case of firstprice auctions, and at least 1 4 in the case of secondprice auctions. These results improve upon the previouslyknown logarithmic bounds, which wereestablished by Hassidim et al. (2011) for firstpriceauctions and by Bhawalkar and Roughgarden (2011) for secondprice auctions. 1
Combinatorial Walrasian Equilibrium
"... We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing str ..."
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Cited by 4 (4 self)
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We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a Combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The difference between a CWE and a (noncombinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation profile admits a CWE that obtains at least half of the optimal (unconstrained) social welfare. Moreover, we devise a polytime algorithm that, given an arbitrary allocation X, computes a CWE that achieves at least half of the welfare of X. Thus, the economic problem of finding a CWE with high social welfare reduces to the algorithmic problem of socialwelfare approximation. In addition, we show that every valuation profile admits a CWE that extracts a logarithmic fraction of the optimal welfare as revenue. Finally, these results are complemented by strong lower bounds when the seller is restricted to using item prices only, which motivates the use of bundles. The strength of our results derives partly from their generality — our results hold for arbitrary valuations that may exhibit complex combinations of substitutes and complements.
On the efficiency of the Walrasian mechanism
 In Proceedings of the 15th ACM Conference on Economics and Computation
, 2014
"... ar ..."
Tight bounds for the price of anarchy of simultaneous first price auctions. arXiv:1312.2371
, 2013
"... We study the Price of Anarchy of simultaneous FirstPrice auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e − 1) [34] and 2 [16], respectively. We provide matching lower bounds for both cases ev ..."
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Cited by 2 (0 self)
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We study the Price of Anarchy of simultaneous FirstPrice auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e − 1) [34] and 2 [16], respectively. We provide matching lower bounds for both cases even for the case of the full information and for mixed Nash equilibria. An immediate consequence of our results, is that for both cases, the Price of Anarchy of these auctions stays the same, for mixed, correlated, coarsecorrelated, and Bayesian Nash equilibria. We bring some novel ideas to the theoretical discussion of upper bounding the Price of Anarchy in Bayesian Auctions settings. We suggest an alternative way to bid against price distributions. Using our approach we were able to reprovide the upper bounds of e/(e − 1) [34] for XOS bidders. An advantage of our approach, is that it reveals a worstcase price distribution, that is used as a building block for the matching lower bound construction. Finally, we apply our techniques on Discriminatory Price multiunit auctions. We complement the results of [13] for the case of subadditive valuations, by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e/(e − 1) using our nonsmooth approach. 1
Simultaneous SingleItem Auctions
"... In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via singleitem auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying singleitem auction. We provide a thorough understanding of the price of anarchy, as ..."
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In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via singleitem auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying singleitem auction. We provide a thorough understanding of the price of anarchy, as a function of the singleitem auction payment rule. When the payment rule depends on the winner’s bid, as in a firstprice auction, we characterize the worstcase price of anarchy in the corresponding CAs with item bidding in terms of a sensitivity measure of the payment rule. As a corollary, we show that equilibrium existence guarantees broader than that of the firstprice rule can only be achieved by sacrificing its property of having only fully efficient (pure) Nash equilibria. For payment rules that are independent of the winner’s bid, we prove a strong optimality result for the canonical secondprice auction. First, its set of pure Nash equilibria is always a superset of that of every other payment rule. Despite this, its worstcase POA is no worse than that of any other payment rule that is independent of the winner’s bid.
On the Complexity of Computing an Equilibrium in Combinatorial Auctions
, 2015
"... We study combinatorial auctions where each item is sold separately but simultaneously via a second price auction. We ask whether it is possible to efficiently compute in this game a pure Nash equilibrium with social welfare close to the optimal one. We show that when the valuations of the bidders ar ..."
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We study combinatorial auctions where each item is sold separately but simultaneously via a second price auction. We ask whether it is possible to efficiently compute in this game a pure Nash equilibrium with social welfare close to the optimal one. We show that when the valuations of the bidders are submodular, in many interesting settings (e.g., constant number of bidders, budget additive bidders) computing an equilibrium with good welfare is essentially as easy as computing, completely ignoring incentives issues, an allocation with good welfare. On the other hand, for subadditive valuations, we show that computing an equilibrium requires exponential communication. Finally, for XOS (a.k.a. fractionally subadditive) valuations, we show that if there exists an efficient algorithm that finds an equilibrium, it must use techniques that are very different from our current ones.
January 2012 Research Statement
"... The last decade has seen a surprisingly rich interplay between economics, computer science, and game theory. From the economics side, the emergence of the Internet as a central platform to conduct trade has created new types of markets, mainly onesided auction markets. These electronic markets shar ..."
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The last decade has seen a surprisingly rich interplay between economics, computer science, and game theory. From the economics side, the emergence of the Internet as a central platform to conduct trade has created new types of markets, mainly onesided auction markets. These electronic markets share many properties with the more classical auction types, on the one hand, but also exhibit several important structural differences. These differences have motivated many studies, aiming to align classic economic theory with the new electronic environment. From the algorithmic side of computer science, the growth of the Internet has lead to new types of distributed agent systems that are characterized by interactions among computers with different ownership and incentives. Many new algorithmic questions are being asked as a result of this development. In contrast to the traditional assumption in computer science, that computers follow protocols and algorithm specifications, we now ask what happens when the input of the algorithm is kept by independent agents, acting selfishly to maximize their own utility. Game theory offers an elegant connection between these two different views, of classical economy vs. classical algorithmic theory. Using gametheoretic tools, a growing community has begun to study models that integrate these two viewpoints to enable a better understanding of the economic aspects of the Internet era. This community consists of researchers from both economics and computer science, demonstrating a fruitful cooperation between the two disciplines. As a researcher, I belong to this community of algorithmic game theorists. In recent years I have been interested in the following four main research directions, with new results as well as ongoing research and intriguing unsolved questions:
Simultaneous auctions are (almost) efficient (Extended Abstract)
"... Simultaneous item auctions are simple and practical procedures for allocating items to bidders with potentially complex preferences. In a simultaneous auction, every bidder submits independent bids on all items simultaneously. The allocation and prices are then resolved for each item separately, bas ..."
Abstract
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Simultaneous item auctions are simple and practical procedures for allocating items to bidders with potentially complex preferences. In a simultaneous auction, every bidder submits independent bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first and secondprice auctions when bidders have complementfree (a.k.a. subadditive) valuations. While it is known that the social welfare of every pure Nash equilibrium (NE) constitutes a constant fraction of the optimal social welfare, a pure NE rarely exists, and moreover, the full information assumption is often unrealistic. Therefore, quantifying the welfare loss in Bayesian Nash equilibria is of particular interest. Previous work established a logarithmic bound on the ratio between the social welfare of a BNE and the expected optimal social welfare in both firstprice auctions (Hassidim et al. [11]) and secondprice auctions (Bhawalkar and Roughgarden [2]), leaving a large gap between a constant and a logarithmic ratio. We introduce a new proof technique and use it to resolve both of these gaps in a unified way. Specifically, we show that the expected social welfare of any BNE is at least 1/2 of the optimal social welfare in the case of firstprice auctions, and at least 1 /4 in the case of secondprice auctions.