Market equilibria with hybrid linear-Leontief utilities

Authors:
Xi Chen;Li-Sha Huang;Shang-Hua Teng
Affiliations:
Institute for Theoretical Computer Science, Tsinghua University, Beijing, China;Institute for Theoretical Computer Science, Tsinghua University, Beijing, China;Computer Science Department, Boston University, Boston, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We introduce a new family of utility functions for exchange markets. This family provides a natural and ''continuous'' hybridization of the traditional linear and Leontief utilities and might be useful in understanding the complexity of computing approximating market equilibria, although computing an equilibrium in a market with this family of utility functions, this is PPAD-hard in general. In this paper, we present an algorithm for finding an approximate Arrow-Debreu equilibrium when the Leontief components of the market are grouped, finite and well-conditioned.