Walrasian Equilibria in Markets with Small Demands

17^th March 2021, 13:00
Themistoklis Melissourgos
Technical University of Munich

Abstract

We study the complexity of finding a Walrasian equilibrium in markets where the agents have k-demand valuations. These valuations are an extension of unit-demand valuations where a bundle's value is the maximum of its k-subsets' values. For unit-demand agents, where the existence of a Walrasian equilibrium is guaranteed, we show that the problem is in quasi-NC. For k=2, we show that it is NP-hard to decide if a Walrasian equilibrium exists even if the valuations are submodular, while for k=3 the hardness carries over to budget-additive valuations. In addition, we give a polynomial-time algorithm for markets with 2-demand single-minded valuations, or unit-demand valuations.

Additional Materials

• https://arxiv.org/abs/2005.11796