research-article

Pricing Equilibria and Graphical Valuations

Authors:

Asuman Ozdaglar,

Pablo ParriloAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 6, Issue 1

Article No.: 2, Pages 1 - 26

https://doi.org/10.1145/3175495

Published: 05 February 2018 Publication History

Abstract

We study pricing equilibria for graphical valuations, whichare a class of valuations that admit a compact representation. These valuations are associated with a value graph, whose nodes correspond to items, and edges encode (pairwise) complementarities/substitutabilities between items. It is known that for graphical valuations a Walrasian equilibrium (a pricing equilibrium that relies on anonymous item prices) does not exist in general. On the other hand, a pricing equilibrium exists when the seller uses an agent-specific graphical pricing rule that involves prices for each item and markups/discounts for pairs of items. We study the existence of pricing equilibria with simpler pricing rules which either (i) require anonymity (so that prices are identical for all agents) while allowing for pairwise markups/discounts or (ii) involve offering prices only for items. We show that a pricing equilibrium with the latter pricing rule exists if and only if a Walrasian equilibrium exists, whereas the former pricing rule may guarantee the existence of a pricing equilibrium even for graphical valuations that do not admit a Walrasian equilibrium. Interestingly, by exploiting a novel connection between the existence of a pricing equilibrium and the partitioning polytope associated with the underlying graph, we also establish that for simple (series-parallel) value graphs, a pricing equilibrium with anonymous graphical pricing rule exists if and only if a Walrasian equilibrium exists. These equivalence results imply that simpler pricing rules (i) and (ii) do not guarantee the existence of a pricing equilibrium for all graphical valuations.

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Cited By

Nguyen TVohra R(2024)(Near-)Substitute Preferences and Equilibria with IndivisibilitiesJournal of Political Economy10.1086/731413132:12(4122-4154)Online publication date: 1-Dec-2024
https://doi.org/10.1086/731413
Borjigin WOta KDong M(2023)Multiple-Walrasian Auction Mechanism for Tree Valuation Service in NFV MarketIEEE Transactions on Computational Social Systems10.1109/TCSS.2022.315169310:1(61-71)Online publication date: Feb-2023
https://doi.org/10.1109/TCSS.2022.3151693
Koizumi H(undefined)Substitutability and Complementarity for EmpiricistsSSRN Electronic Journal10.2139/ssrn.3160118
https://doi.org/10.2139/ssrn.3160118

Index Terms

Pricing Equilibria and Graphical Valuations
1. Applied computing
  1. Operations research
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 6, Issue 1

February 2018

103 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3182630

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

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Copyright © 2018 ACM.

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Publication History

Published: 05 February 2018

Accepted: 01 July 2017

Revised: 01 July 2017

Received: 01 August 2016

Published in TEAC Volume 6, Issue 1

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Cited By

Nguyen TVohra R(2024)(Near-)Substitute Preferences and Equilibria with IndivisibilitiesJournal of Political Economy10.1086/731413132:12(4122-4154)Online publication date: 1-Dec-2024
https://doi.org/10.1086/731413
Borjigin WOta KDong M(2023)Multiple-Walrasian Auction Mechanism for Tree Valuation Service in NFV MarketIEEE Transactions on Computational Social Systems10.1109/TCSS.2022.315169310:1(61-71)Online publication date: Feb-2023
https://doi.org/10.1109/TCSS.2022.3151693
Koizumi H(undefined)Substitutability and Complementarity for EmpiricistsSSRN Electronic Journal10.2139/ssrn.3160118
https://doi.org/10.2139/ssrn.3160118

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