Abstract
In this paper we investigate the structure of prices in approximate solutions to the market equilibrium problem. The bounds achieved allow a scaling approach for computing market equilibrium in the Fisher model. Our algorithm computes an exact solution and improves the complexity of previously known combinatorial algorithms for the problem. It consists of a price roll-back step combined with the auction steps of [11]. Our approach also leads to an efficient polynomial time approximation scheme. We also show a reduction from a flow problem to the market equlibrium problem, illustrating its inherent complexity.
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Arrow, K., Debreu, G.: Existence of an Equilibrium for a Competitive Economy. Econometrica 22, 265–290 (1954)
Arrow, K.J., Black, H.D., Hurwicz, L.: On the Stability of the Competetive Equilibrium, II. Economitrica 27, 82–109 (1959)
Brainard, W.C., Scarf, H.E.: How to Compute Equilibrium Prices in 1891. Cowles Foundation Discussion Paper (1272) (2000)
Codenotti, B., Pemmaraju, S., Varadarajan, K.: A note on the Computation of Equilibria in Exchange Markets with Gross Substitutibility (preprint, 2004)
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), pp. 389–395 (November 2002)
Vazirani, V.V., Devanur, N.R.: 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)
Eaves, B.: A Finite Algorithm for the Linear Exchange Model. Journal of Mathematical Economics 3, 197–203 (1976)
Eisenberg, E.: Aggregation of utility functions. Management Sciences 7(4), 337–350 (1961)
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, Springer, Heidelberg (2004)
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)
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)
Primak, M.E.: A Converging Algorithm for a Linear Exchange Model. Applied Mathematics and Computations 52, 223–231 (1992)
Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26(3), 362–391 (1983)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
Vazirani, V.V.: Market Equilibrium When Buyers Have Spending Constraints (submitted, 2003)
Ye, Y.: A Path to the Arrow-Debreu Competetive Market Equilibrium (preprint, 2004)
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Garg, R., Kapoor, S. (2006). Price Roll-Backs and Path Auctions: An Approximation Scheme for Computing the Market Equilibrium. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_21
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DOI: https://doi.org/10.1007/11944874_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68138-0
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