The Combinatorial World (of Auctions) According to GARP

Boodaghians, Shant; Vetta, Adrian

doi:10.1007/978-3-662-48433-3_10

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…Moreover, in its general form [26,1], the revealed preference rules ensure that the only bidding strategies that are admissible correspond to virtual valuation functions. Indeed, even relaxed implementations of the constraints allow only for approximate virtual valuation functions; see Boodaghians and Vetta [11]. If follows that strategic behavior must take a very restricted form in the CCA, essentially consisting of pre-commiting to a virtual valuation function.…”

Section: Bidding Activity Rulesmentioning

confidence: 99%

On the Economic Efficiency of the Combinatorial Clock Auction

Bousquet

Cai

Hunkenschröder

et al. 2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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Since the 1990s spectrum auctions have been implemented world-wide. This has provided for a practical examination of an assortment of auction mechanisms and, amongst these, two simultaneous ascending price auctions have proved to be extremely successful. These are the simultaneous multiround ascending auction (SMRA) and the combinatorial clock auction (CCA). It has long been known that, for certain classes of valuation functions, the SMRA provides good theoretical guarantees on social welfare. However, no such guarantees were known for the CCA.In this paper, we show that CCA does provide strong guarantees on social welfare provided the price increment and stopping rule are well-chosen. This is very surprising in that the choice of price increment has been used primarily to adjust auction duration and the stopping rule has attracted little attention. The main result is a polylogarithmic approximation guarantee for social welfare when the maximum number of items demanded C by a bidder is fixed. Specifically, we show that either the revenue of the CCA is at least an Ω 1 C 2 log n log 2 m -fraction of the optimal welfare or the welfare of the CCA is at least an Ω 1 log n -fraction of the optimal welfare, where n is the number of bidders and m is the number of items. As a corollary, the welfare ratio -the worst case ratio between the social welfare of the optimum allocation and the social welfare of the CCA allocation -is at most O(C 2 · log n · log 2 m). We emphasize that this latter result requires no assumption on bidders valuation functions. Finally, we prove that such a dependence on C is necessary. In particular, we show that the welfare ratio of the CCA is at least Ω C · log m log log m .

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Section: Bidding Activity Rulesmentioning

confidence: 99%

On the Economic Efficiency of the Combinatorial Clock Auction

Bousquet

Cai

Hunkenschröder

et al. 2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Regardless, the SMRA and the CCA do both incorporate a set of bidding activity rules to encourage truthful bidding. In the CCA these include revealed preference bidding rules that are difficult to game [4,6]. However, the bidding rules in the SMRA are weaker and strategic bidding is common -examples include demand reduction, parking, and hold-up strategies [10].…”

Section: Truthful Bidding In the Smramentioning

confidence: 99%

“…Interestingly, truthful bidding is compatible with the SMRA (for any price trajectories) precisely if the valuation function satisfies the gross substitutes property [20]. The gross substitutes property 6 was defined by Kelso and Crawford [15] and used by them to prove the existence of Walrasian equilibrium. Moreover, with gross substitutes, the SMRA will converge to a Walrasian equilibrium; furthermore such an equilibrium will maximize social welfare (given negligible price increments) -see Milgrom [20,21].…”

Section: Truthful Bidding In the Smramentioning

confidence: 99%

Welfare and Rationality Guarantees for the Simultaneous Multiple-Round Ascending Auction

Bousquet

Cai

Vetta

2015

Web and Internet Economics

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The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Under truthful bidding, the SMRA is known to output a Walrasian equilibrium that maximizes social welfare provided the bidder valuation functions satisfy the gross substitutes property [20]. Recently, it was shown that the combinatorial clock auction (CCA) provides good welfare guarantees for general classes of valuation functions [7]. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.We show the answer is no. But we prove that good welfare guarantees still arise if the degree of complementarities in the bidder valuations are bounded. In particular, if bidder valuations functions are α-near-submodular then, under truthful bidding, the SMRA has a welfare ratio (the worst case ratio between the social welfare of the optimal allocation and the auction allocation) of at most (1 + α). The special case of submodular valuations, namely α = 1, was studied in [12] and produces individually rational solutions. However, for α > 1, this is a bicriteria guarantee, to obtain good welfare under truthful bidding requires relaxing individual rationality. In particular, it necessitates a factor α loss in the degree of individual rationality provided by the auction. We prove this bicriteria guarantee is asymptotically (almost) tight. Truthful bidding, though, is not reasonable assumption in the SMRA [10]. But, bicriteria guarantees continue to hold for natural bidding strategies that are locally optimal. Specifically, the welfare ratio is then at most (1 + α 2 ) and the individual rationality guarantee is again at most α, for α-near submodular valuation functions. These bicriteria guarantees are also (almost) tight. Finally, we examine what strategies are required to ensure individual rationality in the SMRA with general valuation functions. First, we provide a weak characterization, namely secure bidding, for individual rationality. We then show that if the bidders use a profit-maximizing secure bidding strategy the welfare ratio is at most 1 + α. Consequently, by bidding securely, it is possible to obtain the same welfare guarantees as truthful bidding without the loss of individual rationality. Unfortunately, we explain why secure bidding may be incompatible with the auxiliary bidding activity rules that are typically added to the SMRA to reduce gaming.

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“…Most uses of revealed preference as bidding rules in combinatorial auctions (cited above) rely on testing properties of this revealed preference graph. In past work [7,8], we have asked whether such tests, e.g. the minimum feedback vertex set, are efficiently computable.…”

Section: Introductionmentioning

confidence: 99%

Revealed Preference Dimension via Matrix Sign Rank

Boodaghians

2018

Web and Internet Economics

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Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the market dimension is fixed. This paper solves the open problem of determining exactly which graphs are attainable as revealed preference graphs in d-dimensional markets. This is achieved via an exact characterization which closely ties the feasibility of the graph to the Matrix Sign Rank of its signed adjacency matrix. The paper also shows that when the preference relations form a partially ordered set with order-dimension k, the graph is attainable as a revealed preference graph in a k-dimensional market.

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The Combinatorial World (of Auctions) According to GARP

Cited by 3 publications

References 26 publications

On the Economic Efficiency of the Combinatorial Clock Auction

On the Economic Efficiency of the Combinatorial Clock Auction

Welfare and Rationality Guarantees for the Simultaneous Multiple-Round Ascending Auction

Revealed Preference Dimension via Matrix Sign Rank

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