Abstract
We study equilibrium computation for exchange markets. We show that the market equilibrium of either of the following two markets:
-
1
The Fisher market with several classes of concave non-homogeneous utility functions;
-
1
A mixed Fisher and Arrow-Debreu market with homogeneous and log-concave utility functions
can be computed as convex programming and by interior-point algorithms in polynomial time.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arrow, K.J., Debreu, G.: Existence of an Equilibrium for a Competitive Economy. Econometrica 22(3), 265–290 (1954)
Brainard, W.C., Scarf, H.: How to Compute Equilibrium Prices in 1891. Cowles Foundation Discussion Paper 1270 (2000)
Chen, N., Deng, X., Sun, X., Yao, A.C.: Fisher equilibrium price with a class of concave utility functions. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 169–179. Springer, Heidelberg (2004)
Codenotti, B., Pemmaraju, S., Varadarajan, K.: On the polynomial time computation of equilibria for certain exchange economies. In: Proc. SODA 2005 (2005)
Codenotti, B., Saberi, A., Varadarajan, K., Ye, Y.: Leontief Economies Encode Nonzero Sum Two-Player Games. In: Proc. SODA 2006 (2006)
Eisenberg, E., Gale, D.: Consensus of Subjective Probabilities: The Pari-Mutuel Method. Annals of Mathematical Statistics 30, 165–168 (1959)
Eisenberg, E.: Aggregation of Utility Functions. Management Sciences 7(4), 337–350 (1961)
Friedman, J.W.: Concavity of Production Functions and Non-Increasing Returns to Scale. Econometrica 41(5), 981–984 (1973)
Gale, D.: The Theory of Linear Economic Models. McGraw-Hill, New York (1960)
Jain, K., Vazirani, V., Ye, Y.: Market equilibria for homothetic, quasi-concave utilities and economies of scale in production. In: Proc. SODA 2005 (2005)
Scarf, H.E.: The Computation of Economic Equilibria. With collaboration of T. Hansen, Cowles Foundation Monograph No. 24. New Haven: Yale University Press (1973)
Walras, L.: Elements d’economie politique pure; ou, Theorie de la richesse sociale. Elements of Pure Economics; Or the Theory of Social Wealth, Lausanne, Paris (1874)
Ye, Y.: A Path to the Arrow-Debreu Competitive Market Equilibrium. Math Programming (2006)
Ye, Y.: Exchange Market Equilibria with Leontief’s Utility: Freedom of Pricing Leads to Rationality. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, L., Ye, Y., Zhang, J. (2007). A Note on Equilibrium Pricing as Convex Optimization. In: Deng, X., Graham, F.C. (eds) Internet and Network Economics. WINE 2007. Lecture Notes in Computer Science, vol 4858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77105-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-77105-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77104-3
Online ISBN: 978-3-540-77105-0
eBook Packages: Computer ScienceComputer Science (R0)