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We prove that the problem of computing an Arrow-Debreu market equilibrium isPPAD-complete even when all traders use additively separable, piecewise-linearand concave utility functions. In fact, our proof shows that thismarket-equilibrium problem does not have a fully polynomial-time approximationscheme unless every problem in PPAD is solvable in polynomial time.

Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities