Abstract
We propose a new convex optimization formulation for the Fisher market problem with linear utilities. Like the Eisenberg-Gale formulation, the set of feasible points is a polyhedral convex set while the cost function is non-linear; however, unlike that, the optimum is always attained at a vertex of this polytope. The convex cost function depends only on the initial endowments of the buyers. This formulation yields an easy simplex-like pivoting algorithm which is provably strongly polynomial for many special cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adsul, B., Babu, C.S., Garg, J., Mehta, R., Sohoni, M.: Nash equilibria in Fisher market. arXiv:1002.4832 (2010)
Birnbaum, B., Devanur, N.R., Xiao, L.: New convex programs and distributed algorithms for Fisher markets with linear and spending constraint utilities. Working Paper (2010)
Chakraborty, S., Devanur, N.R., Karande, C.: Market equilibrium with transaction costs. arXiv:1001.0393 (2010)
Deng, X., Papadimitriou, C.H., Safra, S.: On the complexity of equilibria. In: STOC 2002 (2002)
Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal-dual type algorithm. JACM 55(5) (2008)
Eisenberg, E., Gale, D.: Consensus of subjective probabilities: The pari-mutuel method. Annals Math. Stat. 30, 165–168 (1959)
Garg, J.: Algorithms for market equilibrium. First APS Report (2008), http://www.cse.iitb.ac.in/~jugal/aps1.pdf
Garg, J.: Fisher markets with transportation costs. Technical Report (2009), http://www.cse.iitb.ac.in/~jugal/techRep.pdf
Jain, K.: A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. In: FOCS 2004 (2004)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Orlin, J.B.: Improved algorithms for computing Fisher’s market clearing prices. In: STOC 2010 (2010)
Shmyrev, V.I.: An algorithm for finding equilibrium in the linear exchange model with fixed budgets. Journal of Applied and Industrial Mathematics 3(4), 505–518 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adsul, B., Babu, C.S., Garg, J., Mehta, R., Sohoni, M. (2010). A Simplex-Like Algorithm for Fisher Markets. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-16170-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16169-8
Online ISBN: 978-3-642-16170-4
eBook Packages: Computer ScienceComputer Science (R0)