Pathways to the optimal set in linear programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
Existence of interior points and interior paths in nonlinear monotone complementarity problems
Mathematics of Operations Research
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
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
A path to the Arrow–Debreu competitive market equilibrium
Mathematical Programming: Series A and B
On the complexity of market equilibria with maximum social welfare
Information Processing Letters
Theoretical Computer Science
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of equilibria: Hardness results for economies via a correspondence with games
Theoretical Computer Science
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
On the approximation and smoothed complexity of Leontief market equilibria
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
A note on equilibrium pricing as convex optimization
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Making economic theory operational
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
ACM Transactions on Algorithms (TALG)
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This paper studies the equilibrium property and algorithmic complexity of the exchange market equilibrium problem with more general utility functions: piece-wise linear functions, which include Leontief’s utility functions. We show that the Fisher model again reduces to the general analytic center problem, and the same linear programming complexity bound applies to approximating its equilibrium. However, the story for the Arrow-Debreu model with Leontief’s utility becomes quite different. We show that, for the first time, that solving this class of Leontief exchange economies is equivalent to solving a known linear complementarity problem whose algorithmic complexity status remains open.