On the Power and Limits of Dynamic Pricing in Combinatorial Markets

Berger, Ben; Eden, Alon; Feldman, Michal

doi:10.1007/978-3-030-64946-3_15

“…It is worth noting that the existence of an optimal scheme reduces to the existence of an appropriate initial price vector; an optimal allocation then can be determined by induction. For a formal definition, we refer the reader to [2].…”

Section: :2 Market Pricing For Matroid Rank Valuationsmentioning

confidence: 99%

“…Gul and Stacchetti [20] later verified that, in a sense, this condition is necessary to ensure the existence of a Walrasian equilibrium. 2 It was first observed by Cohen-Addad et al [8] and Hsu et al [21] that Walrasian prices are not sufficient to control the market, as ties must be broken in a coordinated fashion that is consistent with maximizing social welfare. A natural idea for resolving this issue would be trying to find Walrasian prices where ties do not occur.…”

Section: Previous Workmentioning

confidence: 99%

“…Meanwhile, Hsu et al showed that, under certain conditions, minimal Walrasian equilibrium prices induce low over-demand and high welfare. Recently, Berger et al [2] considered markets beyond unit-demand valuations, and gave a characterization of all optimal allocations in multi-demand markets. Based on this, they provided a polynomial-time algorithm for finding optimal dynamic prices up to three multi-demand buyers.…”

Section: Previous Workmentioning

confidence: 99%

“…Recently, Berger et al [2] investigated the existence of optimal dynamic pricing schemes for k-demand valuations. A valuation v :…”

Section: For Anymentioning

confidence: 99%

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Market Pricing for Matroid Rank Valuations

Bérczi¹,

Kakimura²,

Kobayashi³

2021

SIAM J. Discrete Math.

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“…Recently, Berger et al [2] considered markets beyond unit-demand valuations, and provided a polynomial-time algorithm for finding optimal dynamic prices up to three multi-demand buyers. Their approach is based on a generalization of the relation graph of [8] that they call a 'preference graph', and on a new directed graph termed the 'item-equivalence graph'.…”

Section: Introductionmentioning

confidence: 99%

A dual approach for dynamic pricing in multi-demand markets

Bérczi¹,

Bérczi-Kovács²,

Evelin³

2021

Preprint

0

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Dynamic pricing schemes were introduced as an alternative to posted-price mechanisms. In contrast to static models, the dynamic setting allows to update the prices between buyerarrivals based on the remaining sets of items and buyers, and so it is capable of maximizing social welfare without the need for a central coordinator. In this paper, we study the existence of optimal dynamic pricing schemes in combinatorial markets. In particular, we concentrate on multi-demand valuations, a natural extension of unit-demand valuations. The proposed approach is based on computing an optimal dual solution of the maximum social welfare problem with distinguished structural properties.Our contribution is twofold. By relying on an optimal dual solution, we show the existence of optimal dynamic prices in unit-demand markets and in multi-demand markets up to three buyers, thus giving new interpretations of results of , respectively. Furthermore, we provide an optimal dynamic pricing scheme for bi-demand valuations with an arbitrary number of buyers. In all cases, our proofs also provide efficient algorithms for determining the optimal dynamic prices.

show abstract

A Dual Approach for Dynamic Pricing in Multidemand Markets

Bérczi

¹

,

Bérczi-Kovács

²

,

Evelin

³

2023

SIAM J. Discrete Math.

0

View full text Add to dashboard Cite

Dynamic pricing schemes were introduced as an alternative to posted-price mechanisms. In contrast to static models, the dynamic setting allows to update the prices between buyerarrivals based on the remaining sets of items and buyers, and so it is capable of maximizing social welfare without the need for a central coordinator. In this paper, we study the existence of optimal dynamic pricing schemes in combinatorial markets. In particular, we concentrate on multi-demand valuations, a natural extension of unit-demand valuations. The proposed approach is based on computing an optimal dual solution of the maximum social welfare problem with distinguished structural properties.Our contribution is twofold. By relying on an optimal dual solution, we show the existence of optimal dynamic prices in unit-demand markets and in multi-demand markets up to three buyers, thus giving new interpretations of results of , respectively. Furthermore, we provide an optimal dynamic pricing scheme for bi-demand valuations with an arbitrary number of buyers. In all cases, our proofs also provide efficient algorithms for determining the optimal dynamic prices.

show abstract

On the Power and Limits of Dynamic Pricing in Combinatorial Markets

Cited by 6 publications

References 7 publications

Market Pricing for Matroid Rank Valuations

Market Pricing for Matroid Rank Valuations

A dual approach for dynamic pricing in multi-demand markets

A Dual Approach for Dynamic Pricing in Multidemand Markets

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