Optimal and near-optimal mechanism design with interdependent values

Roughgarden, Tim; Talgam-Cohen, Inbal

doi:10.1145/2482540.2482606

Cited by 18 publications

(39 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We prove that the above impossibility result holds also in the continuous case even if we assume that all of the following conditions simultaneously hold: the valuation distribution is supported everywhere, is entirely symmetric, satisfies regularity, satisfies the monotone hazard rate condition, satisfies affiliation, all the induced marginal distributions have finite expectation, and all the conditional marginal distributions are non-zero everywhere. We remark that Roughgarden and Talgam-Cohen [2013] showed that when all these assumptions are simultaneously satisfied, the optimal ex-post IC and ex-post IR mechanism is the Myerson mechanism, that is the same mechanism that is optimal in the independent value setting. Thus, these conditions make the correlated setting very similar to the independent one with respect to revenue maximization.…”

Section: Non-existence Of Good Posted Price Mechanismsmentioning

confidence: 94%

“…This strengthens our positive results. We refer the interested reader to Roughgarden and Talgam-Cohen [2013] for a further discussion of and comparison between various solution concepts.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…Note that, with this extension, the resulting distribution π does not satisfy the symmetry condition anymore. In the result of Roughgarden and Talgam-Cohen [2013], symmetry is not necessary for the optimality of the Myerson mechanism to hold.…”

Section: Non-existence Of Good Posted Price Mechanismsmentioning

confidence: 99%

“…Segal [2003] give a characterization of optimal ex-post incentive compatible and ex-post individually rational optimal mechanisms. Roughgarden and Talgam-Cohen [2013] study optimal mechanism design in the even more general interdependent setting. They show how to extend the Myerson mechanism to this setting for various assumptions on the valuation distribution.…”

Section: Introductionmentioning

confidence: 99%

“…They show how to extend the Myerson mechanism to this setting for various assumptions on the valuation distribution. There is now a substantial literature [Dobzinski et al, 2011, Roughgarden and Talgam-Cohen, 2013, Chawla et al, 2014, that develop mechanisms with good approximation guarantees for revenue maximization in the correlated setting. These mechanisms build on the lookahead mechanism of Ronen [2001] and thus they also differ from the mechanisms proposed in this work.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sequential Posted Price Mechanisms with Correlated Valuations

Adamczyk

Borodin

Ferraioli

et al. 2015

Web and Internet Economics

View full text Add to dashboard Cite

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to the ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Ω(1/ max{1, d}) fraction of the optimal revenue can be extracted, where d denotes the “degree of dependence” of the valuations, ranging from complete independence (d = 0) to arbitrary dependence (d = n − 1). When we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i, we prove that a constant fraction (2−e√)/4≈0.088 of the optimal revenue can be always extracted

show abstract

Section: Non-existence Of Good Posted Price Mechanismsmentioning

confidence: 94%

“…This strengthens our positive results. We refer the interested reader to Roughgarden and Talgam-Cohen [2013] for a further discussion of and comparison between various solution concepts.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

Section: Non-existence Of Good Posted Price Mechanismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sequential Posted Price Mechanisms with Correlated Valuations

Adamczyk

Borodin

Ferraioli

et al. 2015

Web and Internet Economics

View full text Add to dashboard Cite

show abstract

Limitations of Deterministic Auction Design for Correlated Bidders

Caragiannis

Kaklamanis

Kyropoulou

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

The seminal work of Myerson (Mathematics of OR '81) characterizes incentive-compatible single-item auctions among bidders with independent valuations. In this setting, relatively simple deterministic auction mechanisms achieve revenue optimality. When bidders have correlated valuations, designing the revenue-optimal deterministic auction is a computationally demanding problem; indeed, Papadimitriou and Pierrakos (STOC '11) proved that it is APX-hard, obtaining an explicit inapproximability factor of 1999/2000 = 99.95%. In the current paper, we strengthen this inapproximability factor to 63/64 ≈ 98.5%. Our proof is based on a gap-preserving reduction from the Max-NM 3SAT problem; a variant of the maximum satisfiability problem where each clause has exactly 3 literals and no clause contains both negated and unnegated literals. We furthermore show that the gap between the revenue of deterministic and randomized auctions can be as low as 13/14 ≈ 92.9%, improving an explicit gap of 947/948 ≈ 99.9% by Dobzinski, Fu, and Kleinberg (STOC '11).

show abstract

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

Minooei

Swamy

2013

Web and Internet Economics

View full text Add to dashboard Cite

Optimal and near-optimal mechanism design with interdependent values

Cited by 18 publications

References 32 publications

Sequential Posted Price Mechanisms with Correlated Valuations

Sequential Posted Price Mechanisms with Correlated Valuations

Limitations of Deterministic Auction Design for Correlated Bidders

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

Contact Info

Product

Resources

About