Abstract
We present an auction-based algorithm for the computing market equilibrium prices in a production model, in which producers have a single linear production constraint, and consumers have linear utility functions. We provide algorithms for both the Fisher and Arrow-Debreu versions of the problem.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arrow, K., Debreu, G.: Existence of an Equilibrium for a Competitive Economy. Econometrica 22, 265–290 (1954)
Brainard, W.C., Scarf, H.E.: How to Compute Equilibrium Prices in 1891. Cowles Foundation Discussion Paper (1272) (2000)
Chen, N., Deng, X., Sun, X., Yao, A.: 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., Vardarajan, K.: Equilbrium for Markets with with Leontief Utilities. In: DÃaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 371–382. Springer, Heidelberg (2004)
Deng, X., Papadimitriou, C., Safra, S.: On the Complexity of Equilibria. In: 34th ACM Symposium on Theory of Computing (STOC 2002), Montreal, Quebec, Canada (May 2002)
Devanur, N., Papadimitriou, C., Saberi, A., Vazirani, V.: Market Equilibrium via a Primal-Dual-Type Algorithm. In: 43rd Symposium on Foundations of Computer Science (FOCS 2002), November 2002, pp. 389–395 (2002)
Devanur, N.R., Vazirani, V.: An Improved Approximation Scheme for Computing the Arrow-Debreu Prices for the Linear Case. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 149–155. Springer, Heidelberg (2003)
Devanur, N.R., Vazirani, V.V.: The Spending Constraint Model for Market Equilibrium: Algorithmic, Existence and Uniqueness Results. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (2004)
Eisenberg, E., Gale, D.: Consensus of Subjective Probabilities: The Pari-Mutuel Method. Annals of Mathematical Statistics 30, 165–168 (1959)
Garg, R., Kapoor, S.: Auction Algorithms for Market Equilibrium. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (2004)
Garg, R., Kapoor, S., Vazirani, V.: An Auction-Based Market Equilbrium Algorithm for the Separable Gross Substitutibility Case. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 128–138. Springer, Heidelberg (2004)
Jain, K., Mahdian, M.: Computing equilibria in a fisher market with linear single-constraint production units. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 788–792. Springer, Heidelberg (2005)
Jain, K., Mahdian, M., Saberi, A.: Approximating Market Equilibrium. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 98–108. Springer, Heidelberg (2003)
Jain, K., Vazirani, V.V., Ye, Y.: Market Equilibrium for Homothetic, Quasi-Concave Utilities and economies of scale in production. In: SODA (2005)
Jain, K.: A Polynomial Time Algorithm for Computing the Arrow-Debreau Market equilibrium for Linear Utilities. In: FOCS (2004)
Nenakov, E.I., Primak, M.E.: One algorithm for finding solutions of the Arrow-Debreu model. Kibernetica 3, 127–128 (1983)
Newman, D.J., Primak, M.E.: Complexity of Circumscribed and Inscribed Ellipsod Methods for Solving Equilibrium Economical Models. Applied Mathematics and Computations 52, 223–231 (1992)
Polterovich, V.M.: Economic Equilibrium and the Optimum. Maketon 5, 3–20 (1973)
Primak, M.E.: A Converging Algorithm for a Linear Exchange Model. Journal of Mathematical Economics 22, 181–187 (1993)
Walras, L.: Elements of Pure Economics, or the Theory of Social Wealth, Lausanne, Paris (1874) (in French)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kapoor, S., Mehta, A., Vazirani, V. (2005). An Auction-Based Market Equilibrium Algorithm for a Production Model. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_11
Download citation
DOI: https://doi.org/10.1007/11600930_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30900-0
Online ISBN: 978-3-540-32293-1
eBook Packages: Computer ScienceComputer Science (R0)