Approximating equilibrium under constrained piecewise linear concave utilities with applications to matching markets

Garg, Jugal, Tao, Yixin and Végh, László A. ORCID: 0000-0003-1152-200X (2022) Approximating equilibrium under constrained piecewise linear concave utilities with applications to matching markets. In: Naor, Joseph (Seffi) and Buchbinder, Niv, (eds.) Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2269 - 2284. ISBN 9781611977073

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Abstract

We study the equilibrium computation problem in the Fisher market model with constrained piecewise linear concave (PLC) utilities. This general class captures many well-studied special cases, including markets with PLC utilities, markets with satiation, and matching markets. For the special case of PLC utilities, although the problem is PPAD-hard, Devanur and Kannan (FOCS 2008) gave a polynomial-time algorithm when the number of goods is constant. Our main result is a fixed parameter approximation scheme for computing an approximate equilibrium, where the parameters are the number of agents and the approximation accuracy. This provides an answer to an open question by Devanur and Kannan for PLC utilities, and gives a simpler and faster algorithm for matching markets as the one by Alaei, Jalaly and Tardos (EC 2017). The main technical idea is to work with the stronger concept of thrifty equilibria, and approximating the input utility functions by 'robust' utilities that have favorable marginal properties. With some restrictions, the results also extend to the Arrow-Debreu exchange market model.

Item Type:	Book Section
Official URL:	https://epubs.siam.org/doi/10.1137/1.9781611977073
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	08 Apr 2022 15:00
Last Modified:	09 Nov 2024 17:24
URI:	http://eprints.lse.ac.uk/id/eprint/114635

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