Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd 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
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Auction Algorithms for Market Equilibrium
Mathematics of Operations Research
Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality
Theoretical Computer Science
An auction-based market equilibrium algorithm for a production model
Theoretical Computer Science
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
Computing equilibria in a fisher market with linear single-constraint production units
WINE'05 Proceedings of the First international conference on Internet and Network Economics
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We show a range of complexity results for the Ricardo and Heckscher-Ohlin models of international trade (as Arrow-Debreu production markets). For both models, we show three types of results: 1 When utility functions are Leontief and production functions are linear, it is NP-hard to decide if a market has an equilibrium. 1 When utility functions and production functions are linear, equilibria are efficiently computable (which was already known for Ricardo). 1 When utility functions are Leontief, equilibria are still efficiently computable when the diversity of producers and inputs is limited. Our proofs are based on a general reduction between production and exchange equilibria. One interesting byproduct of our work is a generalization of Ricardo's Law of Comparative Advantage to more than two countries, a fact that does not seem to have been observed in the Economics literature.