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Welfare Guarantees for Combinatorial Auctions with Item Bidding
, 2010
"... We analyze the price of anarchy (POA) in a simple and practical nontruthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate secondprice auctions. We first prove that under a standard “no overbidding ” ..."
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Cited by 17 (2 self)
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We analyze the price of anarchy (POA) in a simple and practical nontruthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate secondprice auctions. We first prove that under a standard “no overbidding ” assumption, for every subadditive valuation profile, every pure Nash equilibrium has welfare at least 50 % of optimal — i.e., the POA is at most 2. For the incomplete information setting, we prove that the POA with respect to BayesNash equilibria is strictly larger than 2 — an unusual separation from the fullinformation model — and is at most 2 ln m, where m is the number of goods.
The Price of Anarchy . . .
, 2012
"... We define smooth games of incomplete information. We prove an “extension theorem ” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect ..."
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Cited by 5 (0 self)
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We define smooth games of incomplete information. We prove an “extension theorem ” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect to a product prior distribution over players ’ preferences. We also note that, for BayesNash equilibria in games with correlated player preferences, there is no general extension theorem for smooth games. We give several applications of our definition and extension theorem. First, we show that many games of incomplete information for which the price of anarchy has been studied are smooth in our sense. Thus our extension theorem unifies much of the known work on the price of anarchy in games of incomplete information. Second, we use our extension theorem to prove new bounds on the price of anarchy of BayesNash equilibria in congestion games with incomplete information.
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 1 (1 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
The Hebrew University
"... We consider two alternatives to optimal auctions: postedprice mechanisms and dynamic auctions. In postedprice mechanisms, the seller posts a single price and sells the item at this price to a bidder that accepts it. In a dynamic auction, bidders arrive sequentially and each bidder leaves the marke ..."
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We consider two alternatives to optimal auctions: postedprice mechanisms and dynamic auctions. In postedprice mechanisms, the seller posts a single price and sells the item at this price to a bidder that accepts it. In a dynamic auction, bidders arrive sequentially and each bidder leaves the market before the next bidder arrives. We establish an exact asymptotic characterization of the optimal revenue in each of these mechanisms for general distributions, under a mild condition taken from extremevalue theory. We also devise postedprice and dynamic mechanisms that achieve this optimal revenue. Intuitively, one would expect auctions to perform better compared to posted prices as the values of the bidders are more dispersed; We show that this intuition holds up to a point where more value dispersion causes an opposite phenomenon. Our results also imply that such mechanisms may lose a nontrivial share of the optimalauction revenue, even in large markets.
APPROXIMATION IN ALGORITHMIC GAME THEORY: ROBUST APPROXIMATION BOUNDS FOR EQUILIBRIA AND AUCTIONS
"... 1.1. Motivation. Many modern computer science applications involve autonomous, selfinterested agents. It is therefore important for us to consider agents ' strategic behavior in modelling the problems, where noncooperative game theory can be very helpful. Unfortunately, as one can expect, strategi ..."
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1.1. Motivation. Many modern computer science applications involve autonomous, selfinterested agents. It is therefore important for us to consider agents ' strategic behavior in modelling the problems, where noncooperative game theory can be very helpful. Unfortunately, as one can expect, strategic behavior of the agents often
Simultaneous SingleItem Auctions
"... Abstract. 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 an ..."
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Abstract. 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. 1
The Dining Bidder Problem: à la russe et à la française
"... Item bidding auctions are a line of research which provides a simple and often efficient alternative to traditional combinatorial auction design in particular, they were inspired by real world auction houses, like eBay and Sotheby’s. We survey the literature from a culinary perspective, offering an ..."
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Item bidding auctions are a line of research which provides a simple and often efficient alternative to traditional combinatorial auction design in particular, they were inspired by real world auction houses, like eBay and Sotheby’s. We survey the literature from a culinary perspective, offering an intuitive illustration of the welfare in simultaneous and sequential auctions. Welfare in simultaneous first and second price auctions is high when bidders have complementfree valuations. In contrast, sequential second price auctions can lead to bad outcomes due to signaling problems and even in the case of first price, a good outcome is only guaranteed for unit demand bidders. We give an intuitive interpretation of an example with bad welfare in sequential first price auctions with submodular bidders from Paes Leme, Syrgkanis and Tardos (SODA’12).