On the Power and Limits of Dynamic Pricing in Combinatorial Markets
We study the power and limits of optimal dynamic pricing in combinatorial markets; i.e., dynamic pricing that leads to optimal social welfare. Previous work by Cohen-Addad et al. [EC’16] demonstrated the existence of optimal dynamic prices for unit-demand buyers, and showed a market with coverage va...
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Published in | Web and Internet Economics pp. 206 - 219 |
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Main Authors | , , |
Format | Book Chapter |
Language | English |
Published |
Cham
Springer International Publishing
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Series | Lecture Notes in Computer Science |
Online Access | Get full text |
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Summary: | We study the power and limits of optimal dynamic pricing in combinatorial markets; i.e., dynamic pricing that leads to optimal social welfare. Previous work by Cohen-Addad et al. [EC’16] demonstrated the existence of optimal dynamic prices for unit-demand buyers, and showed a market with coverage valuations that admits no such prices. However, finding the most general class of markets (i.e., valuation functions) that admit optimal dynamic prices remains an open problem. In this work we establish positive and negative results that narrow the existing gap.
On the positive side, we provide tools for handling markets beyond unit-demand valuations. In particular, we characterize all optimal allocations in multi-demand markets. This characterization allows us to partition the items into equivalence classes according to the role they play in achieving optimality. Using these tools, we provide a poly-time optimal dynamic pricing algorithm for up to 3 multi-demand buyers.
On the negative side, we establish a maximal domain theorem, showing that for every non-gross substitutes valuation, there exist unit-demand valuations such that adding them yields a market that does not admit an optimal dynamic pricing. This result is the dynamic pricing equivalent of the seminal maximal domain theorem by Gul and Stacchetti [JET’99] for Walrasian equilibrium. Yang [JET’17] discovered an error in their original proof, and established a different, incomparable version of their maximal domain theorem. En route to our maximal domain theorem for optimal dynamic pricing, we provide the first complete proof of the original theorem by Gul and Stacchetti. |
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Bibliography: | This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 866132), and by the Israel Science Foundation (grant number 317/17). The work of A. Eden was supported by the National Science Foundation under Grant No. CCF-1718549. |
ISBN: | 3030649458 9783030649456 |
ISSN: | 0302-9743 1611-3349 |
DOI: | 10.1007/978-3-030-64946-3_15 |