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Pricing Equilibria and Graphical Valuations

Pricing Equilibria and Graphical Valuations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation (TEAC) Association for Computing Machinery

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2018 ACM
ISSN
2167-8375
eISSN
2167-8383
DOI
10.1145/3175495
Publisher site
See Article on Publisher Site

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.

Journal

ACM Transactions on Economics and Computation (TEAC)Association for Computing Machinery

Published: Feb 5, 2018

Keywords: Pricing equilibrium

References