Simple Mechanisms for Agents with Complements

Feldman, Michal; Friedler, Ophir; Morgenstern, Jamie; Reiner, Guy

doi:10.1145/2940716.2940735

Cited by 9 publications

(21 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, recent results seem to suggest, that there exists smooth transitions from complement-free to completely arbitrary monotone set functions, parametrized by the degree of complementarity of the function. The transitions support graceful degrading of the approximation ratio for various combinatorial optimization tasks (Feige and Izsak 2013;Feldman and Izsak 2014;Feige et al 2015;Chen, Teng, and Zhang 2019), and the revenue and efficiency (measured by the Price of Anarchy) of well-studied simple protocols for combinatorial auctions (Feige et al 2015;Feldman et al 2016;Eden et al 2017;Chen, Teng, and Zhang 2019).…”

Section: Introductionmentioning

confidence: 79%

See 1 more Smart Citation

Learning Set Functions with Limited Complementarity

Zhang

2019

AAAI

View full text Add to dashboard Cite

We study PMAC-learning of real-valued set functions with limited complementarity. We prove, to our knowledge, the first nontrivial learnability result for set functions exhibiting complementarity, generalizing Balcan and Harvey’s result for submodular functions. We prove a nearly matching information theoretical lower bound on the number of samples required, complementing our learnability result. We conduct numerical simulations to show that our algorithm is likely to perform well in practice.

show abstract

Section: Introductionmentioning

confidence: 79%

“…Beside the SD and the SMW hierarchies, there are several other measures of complementarity, among which two most useful ones are Maximum-over-Positive-Hypergraphs (MPH) (Feige et al 2015) and its variant, Maximum-over-Positive-Supermodular (MPS) (Feldman et al 2016).…”

Section: Additional Related Workmentioning

confidence: 99%

Learning Set Functions with Limited Complementarity

Zhang

2019

AAAI

View full text Add to dashboard Cite

show abstract

“…If the designer desires dominant strategy truthfulness but is okay with an average-case welfare guarantee, then a 1/2-approximation is known for XOS bidders [33]. Combinatorial auctions have also been studied through the lens of Price of Anarchy, but a deeper discussion of this is outside the scope of this paper [6,45,51,52,32,9,20,15,41,11,7,31].…”

Section: A Background On Related Workmentioning

confidence: 99%

On Simultaneous Two-player Combinatorial Auctions

Braverman

Mao

Weinberg

2018

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

View full text Add to dashboard Cite

We consider the following communication problem: Alice and Bob each have some valuation functions v 1 (·) and v 2 (·) over subsets of m items, and their goal is to partition the items into S,S in a way that maximizes the welfare, v 1 (S)+v 2 (S). We study both the allocation problem, which asks for a welfare-maximizing partition and the decision problem, which asks whether or not there exists a partition guaranteeing certain welfare, for binary XOS valuations. For interactive protocols with poly(m) communication, a tight 3/4-approximation is known for both [29,23].For interactive protocols, the allocation problem is provably harder than the decision problem: any solution to the allocation problem implies a solution to the decision problem with one additional round and log m additional bits of communication via a trivial reduction. Surprisingly, the allocation problem is provably easier for simultaneous protocols. Specifically, we show:• There exists a simultaneous, randomized protocol with polynomial communication that selects a partition whose expected welfare is at least 3/4 of the optimum. This matches the guarantee of the best interactive, randomized protocol with polynomial communication.• For all ε > 0, any simultaneous, randomized protocol that decides whether the welfare of the optimal partition is ≥ 1 or ≤ 3/4 − 1/108 + ε correctly with probability > 1/2 + 1/poly(m) requires exponential communication. (≤ 3/4 − 1/108) protocols with polynomial communication. In other words, this trivial reduction from decision to allocation problems provably requires the extra round of communication. We further discuss the implications of our results for the design of truthful combinatorial auctions in general, and extensions to general XOS valuations. In particular, our protocol for the allocation problem implies a new style of truthful mechanisms. IntroductionIntuitively, search problems (find the optimal solution) are considered "strictly harder" than decision problems (does a solution with quality ≥ Q exist?) for the following (formal) reason: once you find the optimal solution, you can simply evaluate it and check whether its quality is ≥ Q or not. The same intuition carries over to approximation as well: once you find a solution whose quality is within a factor α of optimal, you can distinguish between cases where solutions with quality ≥ Q exist and those where all solutions have quality ≤ αQ. The easy conclusion one then draws is that the communication (resp. runtime) required for an α-approximation to any decision problem is upper bounded by the communication (resp. runtime) required for an α-approximation to the corresponding search problem plus the communication (resp. runtime) required to evaluate the quality of a proposed solution.Note though that for communication problems, in addition to the negligible increase in communication (due to evaluating the quality of the proposed solution), this simple reduction might also require (at least) an extra round of communication (because the parties can evalua...

show abstract

“…Buyers with Complements. Even for the traditionally simpler domain of welfare maximization, the state-of-the-art only recently has begun designing mechanisms for buyers with complements [1,20,24,22]. The main difficulty is that horrible lower bounds are known for general valuations [37], so in order to get interesting positive results, some assumptions are necessary on the degree to which buyer valuations exhibit substitutes or complements.…”

Section: Introductionmentioning

confidence: 99%

“…The main difficulty is that horrible lower bounds are known for general valuations [37], so in order to get interesting positive results, some assumptions are necessary on the degree to which buyer valuations exhibit substitutes or complements. Interestingly, good positive results are possible in the complete absence of complements and no restriction on the degree of substitutability [17,16,19,23,15], but not vice versa: many strong lower bounds still exist in the absence of substitutes but with arbitrary complementarity [33,1,35,22].…”

Section: Introductionmentioning

confidence: 99%

A Simple and Approximately Optimal Mechanism for a Buyer with Complements

Eden¹,

Feldman²,

Friedler³

et al. 2016

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a revenue-maximizing seller with m heterogeneous items and a single buyer whose valuation v for the items may exhibit both substitutes (i.e., for some S, T , v(S ∪ T ) < v(S) + v(T )) and complements (i.e., for some S, T , v(S ∪ T ) > v(S) + v(T )). We show that the mechanism first proposed by Babaioff et al. [2014] -the better of selling the items separately and bundling them together -guarantees a Θ(d) fraction of the optimal revenue, where d is a measure on the degree of complementarity. Note that this is the first approximately optimal mechanism for a buyer whose valuation exhibits any kind of complementarity, and extends the work of Rubinstein and Weinberg [2015], which proved that the same simple mechanisms achieve a constant factor approximation when buyer valuations are subadditive, the most general class of complement-free valuations.Our proof is enabled by the recent duality framework developed in Cai et al. [2016], which we use to obtain a bound on the optimal revenue in this setting. Our main technical contributions are specialized to handle the intricacies of settings with complements, and include an algorithm for partitioning edges in a hypergraph. Even nailing down the right model and notion of "degree of complementarity" to obtain meaningful results is of interest, as the natural extensions of previous definitions provably fail.

show abstract

Simple Mechanisms for Agents with Complements

Cited by 9 publications

References 42 publications

Learning Set Functions with Limited Complementarity

Learning Set Functions with Limited Complementarity

On Simultaneous Two-player Combinatorial Auctions

A Simple and Approximately Optimal Mechanism for a Buyer with Complements

Contact Info

Product

Resources

About