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Pricing Equilibria and Graphical Valuations

Author(s)
Candogan, Utku Ozan; Ozdaglar, Asuman; Parrilo, Pablo A.
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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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 aWalrasian 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 aWalrasian 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.
Date issued
2018-02
URI
https://hdl.handle.net/1721.1/121505
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
ACM transactions on economics and computation
Publisher
Association for Computing Machinery (ACM)
Citation
Candogan, Ozan, Asuman Ozdaglar and Pablo Parrilo. "Pricing Equilibria and Graphical Valuations." ACM transactions on economics and computation 6, issue 1 (March 2018): Article 2.
Version: Author's final manuscript
ISSN
2167-8383
2167-8375

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