On Simultaneous Two-player Combinatorial Auctions

Braverman, Mark; Mao, Jieming; Weinberg, S. Matthew

doi:10.1137/1.9781611975031.146

Cited by 13 publications

(42 citation statements)

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“…This problem is provably easier than finding an approximate allocation in the interactive setting: any r-round protocol for finding an approximate allocation can be used to obtain an (r + 1)-round protocol for estimating the value of social welfare with O(n) additional communication; simply compute the approximate allocation in the first r rounds and spend one additional round in which each player declares her value for the assigned bundle to the referee. It was shown very recently in [6] that this loss of one round in the reduction is unavoidable (see Section 3 for further details). However, this extra one round is essentially negligible for our purpose as we are interested in the asymptotic dependence of the approximation ratio and the number of rounds.…”

Section: Communication Modelmentioning

confidence: 99%

Combinatorial Auctions Do Need Modest Interaction

AssadiSepehr

2020

ACM Trans. Econ. Comput.

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We study the necessity of interaction for obtaining efficient allocations in combinatorial auctions with subadditive bidders. This problem was originally introduced by Dobzinski, Nisan, and Oren [9] as the following simple market scenario: m items are to be allocated among n bidders in a distributed setting where bidders valuations are private and hence communication is needed to obtain an efficient allocation. The communication happens in rounds: in each round, each bidder, simultaneously with others, broadcasts a message to all parties involved. At the end, the central planner computes an allocation solely based on the communicated messages. Dobzinski et al. [9] showed that (at least some) interaction is necessary for obtaining any efficient allocation: no non-interactive (1-round) protocol with polynomial communication (in the number of items and bidders) can achieve approximation ratio better than Ω(m 1/4 ), while for any r ≥ 1, there exists r-round protocols that achieve O(r · m 1/r+1 ) approximation with polynomial communication; in particular, O(log m) rounds of interaction suffice to obtain an (almost) efficient allocation, i.e., a polylog(m)-approximation.A natural question at this point is to identify the "right" level of interaction (i.e., number of rounds) necessary to obtain an efficient allocation. In this paper, we resolve this question by providing an almost tight round-approximation tradeoff for this problem: we show that for any r ≥ 1, any r-round protocol that uses poly(m, n) bits of communication can only approximate the social welfare up to a factor of Ω( 1 r · m 1/2r+1 ). This in particular implies that Ω( log m log log m ) rounds of interaction are necessary for obtaining any efficient allocation (i.e., a constant or even a polylog(m)-approximation) in these markets. Our work builds on the recent multi-party round-elimination technique of Alon, Nisan, Raz, and Weinstein [2] -used to prove similar-inspirit lower bounds for round-approximation tradeoff in unit-demand (matching) markets -and settles an open question posed by Dobzinski et al. [9] and Alon et al. [2].

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Section: Communication Modelmentioning

confidence: 99%

Combinatorial Auctions Do Need Modest Interaction

AssadiSepehr

2020

ACM Trans. Econ. Comput.

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“…More formally, a δ-error α-approximation protocol needs to, for each input instance I sampled from D, output a number in the range [ This problem is provably easier than finding an approximate allocation in the interactive setting: any r-round protocol for finding an approximate allocation can be used to obtain an (r + 1)-round protocol for estimating the value of social welfare with O(n) additional communication; simply compute the approximate allocation in the first r rounds and spend one additional round in which each player declares her value for the assigned bundle to the referee. It was shown very recently in [6] that this loss of one round in the reduction is unavoidable (see Section 3 for further details). However, this extra one round is essentially negligible for our purpose as we are interested in the asymptotic dependence of the approximation ratio and the number of rounds.…”

Section: Communication Modelmentioning

confidence: 99%

“…The reason is that while the problem of estimating the social welfare is provably easier than the problem of finding an approximate allocation, the reduction requires one additional round of interaction and hence, in general, a simultaneous protocol for the problem of finding the allocation only implies a 2-round (and not a simultaneous) protocol for the social welfare estimation problem 3 . Interestingly, for the case of n = 2 players, Braverman et al [6] very recently showed that the problem of estimating the social welfare is indeed provably harder than finding an approximate allocation for simultaneous protocols. In the light of this result, it seems plausible that one can indeed improve the protocol of [9] and find an O(m 1/4 )-approximation protocol for finding an approximate allocation (matching the lower bound of [9]); however, Theorem 1 suggests that if such a protocol exists, it necessarily should be oblivious to the welfare of the allocation it provides.…”

Section: Warm Up: a Lower Bound For Simultaneous Protocolsmentioning

confidence: 99%

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Combinatorial Auctions Do Need Modest Interaction

Assadi

2017

Proceedings of the 2017 ACM Conference on Economics and Computation

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We study the necessity of interaction for obtaining efficient allocations in combinatorial auctions with subadditive bidders. This problem was originally introduced by Dobzinski, Nisan, and Oren [9] as the following simple market scenario: m items are to be allocated among n bidders in a distributed setting where bidders valuations are private and hence communication is needed to obtain an efficient allocation. The communication happens in rounds: in each round, each bidder, simultaneously with others, broadcasts a message to all parties involved. At the end, the central planner computes an allocation solely based on the communicated messages. Dobzinski et al. [9] showed that (at least some) interaction is necessary for obtaining any efficient allocation: no non-interactive (1-round) protocol with polynomial communication (in the number of items and bidders) can achieve approximation ratio better than Ω(m 1/4 ), while for any r ≥ 1, there exists r-round protocols that achieve O(r · m 1/r+1 ) approximation with polynomial communication; in particular, O(log m) rounds of interaction suffice to obtain an (almost) efficient allocation, i.e., a polylog(m)-approximation.A natural question at this point is to identify the "right" level of interaction (i.e., number of rounds) necessary to obtain an efficient allocation. In this paper, we resolve this question by providing an almost tight round-approximation tradeoff for this problem: we show that for any r ≥ 1, any r-round protocol that uses poly(m, n) bits of communication can only approximate the social welfare up to a factor of Ω(). This in particular implies that Ω( log m log log m ) rounds of interaction are necessary for obtaining any efficient allocation (i.e., a constant or even a polylog(m)-approximation) in these markets. Our work builds on the recent multi-party round-elimination technique of Alon, Nisan, Raz, and Weinstein [2] -used to prove similar-inspirit lower bounds for round-approximation tradeoff in unit-demand (matching) markets -and settles an open question posed by Dobzinski et al. [9] and Alon et al. [2].

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“…This has led the researchers to study the communication complexity of this problem that can capture arbitrary queries to valuations [3-5, 12-14, 18, 22, 36, 37]. Although a clear path for proving a separation between the communication complexity of truthful mechanisms and general algorithms was shown recently in [12] (see also [5,22]), no such separation is still known.…”

Section: Introductionmentioning

confidence: 99%

Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

Assadi

Singla

2019

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)

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A longstanding open problem in Algorithmic Mechanism Design is to design computationallyefficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an O(log 2 m)-approximation where m is the number of items. This problem has been studied extensively since, culminating in an O( √ log m)-approximation mechanism by Dobzinski [STOC'16].We present a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor. In particular, our mechanism achieves an O((log log m) 3 )-approximation in expectation, uses only O(n) demand queries, and has universal truthfulness guarantee. This settles an open question of Dobzinski on whether Θ( √ log m) is the best approximation ratio in this setting in negative.

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On Simultaneous Two-player Combinatorial Auctions

Cited by 13 publications

References 50 publications

Combinatorial Auctions Do Need Modest Interaction

Combinatorial Auctions Do Need Modest Interaction

Combinatorial Auctions Do Need Modest Interaction

Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

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