United Kingdom

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&#39;s value is the maximum of its  k -subsets&#39; 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.

AAMAS 2021

Walrasian Equilibria in Markets with Small Demands

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2022

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.

technical paper

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