Combinatorial Walrasian Equilibrium

8 years 18 days ago

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We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a Combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The diﬀerence between a CWE and a (non-combinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation proﬁle admits a CWE that obtains at least half of the optimal (unconstrained) social welfare. Moreover, we devise a poly-time algorithm that, given an arbitrary allocation X, computes a CWE that achieves at least half of the we...

Michal Feldman, Nick Gravin, Brendan Lucier

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