The computation of approximate competitive equilibrium is PPAD-hard

Authors:
Xiaotie Deng;Ye Du
Affiliations:
Department of Computer Science, City University of Hong Kong, Hong Kong SAR;Department of Electrical Engineering and Computer Science, University of Michigan, 2260 Hayward Ave, Ann Arbor, MI 48109-2121, USA
Venue:
Information Processing Letters
Year:
2008

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Abstract

Arrow and Debreu showed in 1954 that, under mild conditions, a competitive economy always has an equilibrium. In this paper, we show that, given a competitive economy that fully respects all the conditions of Arrow-Debreu's existence theorem, for any positive constant h0, it is PPAD-hard to compute a 1n^h-approximate competitive equilibrium.