Volume 12 (2016) Article 20 pp. 1-25
Dichotomies in Equilibrium Computation and Membership of PLC Markets in FIXP
by
Revised: July 16, 2016
Published: December 30, 2016
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Piecewise-linear, concave (PLC) utility functions play an important role in work done at the intersection of economics and algorithms. We prove that the problem of computing an equilibrium in Arrow-Debreu markets with PLC utilities and PLC production sets is in the class $\textsf{FIXP}$. Recently it was shown that these problems are also $\textsf{FIXP}$-hard (Garg et al., arXiv:1411.5060), hence settling the long-standing question of the complexity of this problem. Central to our proof is capturing equilibria of these markets as fixed points of a continuous function via a nonlinear complementarity problem (NCP) formulation.