On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Auction algorithms for market equilibrium
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the polynomial time computation of equilibria for certain exchange economies
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality
Theoretical Computer Science
A path to the Arrow–Debreu competitive market equilibrium
Mathematical Programming: Series A and B
Algorithmic Game Theory
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
Market Equilibria in Polynomial Time for Fixed Number of Goods or Agents
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On the approximation and smoothed complexity of Leontief market equilibria
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Market equilibria with hybrid linear-leontief utilities
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Market equilibrium for CES exchange economies: existence, multiplicity, and computation
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Spending Constraint Utilities with Applications to the Adwords Market
Mathematics of Operations Research
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It
Mathematics of Operations Research
The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The notion of a rational convex program, and an algorithm for the arrow-debreu Nash bargaining game
Journal of the ACM (JACM)
A complementary pivot algorithm for markets under separable, piecewise-linear concave utilities
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The complexity of non-monotone markets
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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It is a common belief that computing a market equilibrium in Fisher's spending model is easier than computing a market equilibrium in Arrow-Debreu's exchange model. This belief is built on the fact that we have more algorithmic success in Fisher equilibria than Arrow-Debreu equilibria. For example, a Fisher equilibrium in a Leontief market can be found in polynomial time, while it is PPAD-hard to compute an approximate Arrow-Debreu equilibrium in a Leontief market.In this paper, we show that even when all the utilities are additively separable, piecewise-linear and concave, computing an approximate equilibrium in Fisher's model is PPAD-hard. Our result solves a long-term open question on the complexity of market equilibria. To the best of our knowledge, this is the first PPAD-hardness result for Fisher's model.