We prove that the problem of computing an Arrow-Debreu market equilibrium is PPAD-complete even when all traders use additively separable, piecewise-linear and concave utility functions. In fact, our proof shows that this market-equilibrium problem does not have a fully polynomial-time approximation scheme, unless every problem in PPAD is solvable in polynomial time.
Chen et al. REF showed that the problem of computing an Arrow-Debreu market equilibrium with additively separable utilities is PPADcomplete.
Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities
2009 50th Annual IEEE Symposium on Foundations of Computer Science
2009 50th Annual IEEE Symposium on Foundations of Computer Science
Mathematics Computer Science