Abstract
We consider the Arrow-Debreu competitive market equilibrium problem which was first formulated by Leon Walras in 1874 [12]. In this problem every one in a population of n players has an initial endowment of a divisible good and a utility function for consuming all goods—own and others. Every player sells the entire initial endowment and then uses the revenue to buy a bundle of goods such that his or her utility function is maximized. Walras asked whether prices could be set for everyone’s good such that this is possible. An answer was given by Arrow and Debreu in 1954 [1] who showed that such equilibrium would exist if the utility functions were concave. Their proof was non-constructive and did not offer any algorithm to find such equilibrium prices.
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References
Arrow, K., Debreu, G.: Existence of a competitive equilibrium for a competitive economy. Econometrica 22(3), 265–290 (1954)
Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper 1270 (2000)
Codenotti, B., Varadarajan, K.: Efficient computation of equilibrium prices for market with Leontief utilities. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 371–382. Springer, Heidelberg (2004)
Cottle, R., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. In: Interior–point methods,ch. 5.9, pp. 461–475. Academic Press, Boston (1992)
Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal-dual-type algorithm. In: The 43rd Annual IEEE Symposium on Foundations of Computer Science, pp. 389–395 (2002); Journal version on http://www.cc.gatech.edu/~saberi/ (2004)
Eisenberg, E., Gale, D.: Consensus of subjective probabilities: The pari-mutuel method. Annals Of Mathematical Statistics 30, 165–168 (1959)
Eaves, B.C.: A finite algorithm for the linear exchange model. J. of Mathematical Economics 3, 197–203 (1976)
Gale, D.: The Theory of Linear Economic Models. McGraw Hill, N.Y (1960)
Jain, K.: A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. Discussion paper, Microsoft Lab, Seattle, WA (2003)
Nenakhov, E., Primak, M.: About one algorithm for finding the solution of the arrow-debreu model. Kibernetica (3), 127–128 (1983)
Nesterov, Y.E., Nemirovskii, A.S.: Interior Point Polynomial Methods in Convex Programming Theory and Algorithms. SIAM Publications, Philadelphia (1993)
Walras, L.: Elements of Pure Economics, or the Theory of Social Wealth (1874); (1899, 4th edn.; 1926, rev. edn., 1954, Engl. Transl.)
Ye, Y.: A Path to the Arrow-Debreu Competitive Matket Equilibrium, Stanford, CA 94305, USA, Working paper, posted, February 23 (2004), www.stanford.edu/~yyye
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Ye, Y. (2005). Computing the Arrow-Debreu Competitive Market Equilibrium and Its Extensions. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_2
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DOI: https://doi.org/10.1007/11496199_2
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