Communication Complexity of Combinatorial Auctions with Submodular Valuations

Dobzinski, Shahar; Vondrák, Jan

doi:10.1137/1.9781611973105.87

Cited by 24 publications

(17 citation statements)

References 27 publications

(65 reference statements)

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“…This is consistent with our exponential lower bound, as it is well known that finding the leximin solution can require exponential time for general valuations (e.g. [15]). …”

Section: Positive Efx Resultssupporting

confidence: 91%

Almost Envy-Freeness with General Valuations

Plaut¹,

Roughgarde²

2018

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

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The goal of fair division is to distribute resources among competing players in a "fair" way. Envy-freeness is the most extensively studied fairness notion in fair division. Envy-free allocations do not always exist with indivisible goods, motivating the study of relaxed versions of envy-freeness. We study the envy-freeness up to any good (EFX) property, which states that no player prefers the bundle of another player following the removal of any single good, and prove the first general results about this property. We use the leximin solution to show existence of EFX allocations in several contexts, sometimes in conjunction with Pareto optimality. For two players with valuations obeying a mild assumption, one of these results provides stronger guarantees than the currently deployed algorithm on Spliddit, a popular fair division website. Unfortunately, finding the leximin solution can require exponential time. We show that this is necessary by proving an exponential lower bound on the number of value queries needed to identify an EFX allocation, even for two players with identical valuations. We consider both additive and more general valuations, and our work suggests that there is a rich landscape of problems to explore in the fair division of indivisible goods with different classes of player valuations.

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“…This is consistent with our exponential lower bound, as it is well known that finding the leximin solution can require exponential time for general valuations (e.g. [15]). …”

Section: Positive Efx Resultssupporting

confidence: 91%

Almost Envy-Freeness with General Valuations

Plaut¹,

Roughgarde²

2018

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

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“…It is known that obtaining a better than (1 − 1/2e)-approximation to social welfare in submodular combinatorial auctions requires exponential communication [12] (regardless of the number of rounds of interaction). However, no better lower bounds are known for bounded-round protocols (even for simultaneous ones).…”

Section: Resultsmentioning

confidence: 99%

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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“…A particular case of this problem that has received significant attention is when the valuation functions of all the bidders are submodular 1 (see, e.g. [9][10][11][15][16][17][18]25,31,33] and references therein). There is no poly-time algorithm for finding the optimal allocation of submodular bidders [18,25,34] and thus VCG mechanism is not computationally-efficient here.…”

Section: Introductionmentioning

confidence: 99%

“…[9][10][11][15][16][17][18]25,31,33] and references therein). There is no poly-time algorithm for finding the optimal allocation of submodular bidders [18,25,34] and thus VCG mechanism is not computationally-efficient here. On the other hand, by using only value queries, a simple greedy algorithm can achieve a 2-approximation [33] and this can be further improved to ( e e−1 )-approximation [41], and even slightly better [24] by using demand queries.…”

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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Communication Complexity of Combinatorial Auctions with Submodular Valuations

Cited by 24 publications

References 27 publications

Almost Envy-Freeness with General Valuations

Almost Envy-Freeness with General Valuations

Combinatorial Auctions Do Need Modest Interaction

Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

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