Abstract
Utility functions satisfying gross substitutability have been studied extensively in the economics literature [1,11,12] and recently, the importance of this property has been recognized in the design of combinatorial polynomial time market equilibrium algorithms [8]. This naturally raises the following question: is it possible to design a combinatorial polynomial time algorithm for this general class of utility functions? We partially answer this question by giving an algorithm for separable, differentiable, concave utility functions satisfying gross substitutes. Our algorithm uses the auction based approach of [10].
We also outline an extension of our method to the Walrasian model.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arrow, K., Block, H., Hurwicz, L.: On the stability of the competitive equilibrium, II. Econometrica 27(1), 82–109 (1959)
Bansal, V., Garg, R.: Simultaneous Independent Online Auctions with Discrete Bid Increments. Electronic Commerce Research Journal: Special issue on Dynamic Pricing Policies in Electronic Commerce (to appear)
Bertsekas, D.P.: Auction Algorithms for Network Flow Problems: A Tutorial Introduction. Computational Optimization and Applications 1, 7–66 (1992)
Demange, G., Gale, D., Sotomayor, M.: Multi-item Auctions. Journal of Political Economy 94(4), 863–872 (1986)
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)
Greenberg, J.: An elementary proof of the existence of a competitive equilibrium with weak gross substitutes. The Quarterly Journal of Economics 91, 513–516 (1977)
Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87, 95–124 (1999)
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.: A Polynomial Time Algorithm for Computing the Arrow-Debreau Market equilibrium for Linear Utilities (preprint)
Kuhn, H.W.: The Hungarian Method for the Assignment Problem. Naval Research Logistics Quarterly 2, 83–97 (1955)
Papadimtriou, C.: Algorithms, games, and the internet. In: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, pp. 749–753 (2001)
Vazirani, V.V.: Market Equilibrium When Buyers Have Spending Constraints (2003) (submitted)
Ye, Y.: A Path to the Arrow-Debreu Competetive Market Equilibrium (2004) (preprint)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Garg, R., Kapoor, S., Vazirani, V. (2004). An Auction-Based Market Equilibrium Algorithm for the Separable Gross Substitutability Case. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-27821-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22894-3
Online ISBN: 978-3-540-27821-4
eBook Packages: Springer Book Archive