Four aspects of the mathematical theory of economic equilibrium

G. Debreu

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 32 (1977) no. 1

Bibliographie

[1] K. J. Arrow, “Le rôle des valeurs boursières pour la répartition la meilleure des risques”, Econométrie, 1953, 41–47 ; discussion, 1953, 47–48; Colloq. Internat. Centre National de la Recherche Scientifique, no. 40, Paris, 1952; Centre de la Recherche Scientifique, Paris, 1953; Review of Economic Studies, 31 (1964), 91–96, MR 16, 943 | MR | DOI

[2] K. J. Arrow, G. Debreu, “Existence of an equilibrium for a competitive economy”, Econometrica, 22 (1954), 265–290, MR 17, 985 | DOI | MR | Zbl

[3] K. J. Arrow, F. H. Hahn, General competitive analysis, Holden-Day, San Francisco, California, 1971 | MR | Zbl

[4] R. J. Aumann, “Markets with a continuum of traders”, Econometrica, 32 (1964), 39–50, MR 30, 2908 | DOI | MR | Zbl

[5] Y. Balasko, “On the graph of the Walras correspondence”, Econometrica, 000 (1974) | MR

[6] Y. Balasko, “Some results on uniqueness and on stability of equilibrium in general equilibrium theory”, J. Math. Economics, 2 (1974), 95–118 | DOI | MR

[7] F. E. Browder, “On continuity of fixed points under deformations of continuous mappings”, Summa Brasil Math., 4 (1960), 183–191, MR 24, A543 | MR | Zbl

[8] F. Delbaen, Lower and upper hemi-continuity of the walras correspondence, Doctoral disseration, Free University of Brussels, 1971

[9] E. Dierker, Topological methods in Walrasian economics, Lecture Notes in Economics and Mathematical Systems, 92, Springer-Verlag, Berlin, 1974 | MR | Zbl

[10] E. Dierker, H. Dierker, “On the local uniqueness of equilibria”, Econometrica, 40 (1972), 867–881 | DOI | MR | Zbl

[11] H. Dierker, “Smooth preferences and the regularity of equilibria”, J. Math. Economics, 2 (1975), 43–62 | DOI | MR | Zbl

[12] B. C. Eaves, “Homotopies for computation of fixed points”, Math. Programming, 3 (1972), 1–22, MR 46, 3089 | DOI | MR | Zbl

[13] B. C. Eaves, “Properly labeled simplexes”, Studies in Optimization, MAA Studies in Mathematics, 10, eds. G. B. Dantzig, B. C. Eaves, Prentice-Hall, 1974 | MR

[14] F. Y. Edgeworth, Mathematical psychics, Paul Kegan, London, 1881

[15] D. Gale, “The law of supply and demand”, Math. Scand., 3 (1955), 155–169, MR 17, 985 | MR | Zbl

[16] B. Grodal, “The rate of convergence of the core for a purely competitive sequence of economies”, J. Math. Economics, 2 (1975), 171–186 | DOI | MR | Zbl

[17] T. Hansen, On the approximation of a competitive equilibrium, Ph. D. Dissertation, Yale University, New Haven, Conn., 1968

[18] F. Hausdorff, Set theory, Chelsea, New York, 1957, MR 19, 111 | MR | Zbl

[19] K. Hildenbraund, Finiteness of $\pi(e)$ and continuity of $\pi$, Appendix to Chapter 2 in W. Hildenbrand [20]

[20] W. Hildenbrand, Core and equilibria of a large economy, Princeton Univ. Press, Princeton, N. J., 1974 | MR | Zbl

[21] S. Kakutani, “A generalization of Brouwer's fixed point theorem”, Duke Math. J., 8 (1941), 457–459, MR 3, 60 | DOI | MR | Zbl

[22] Y. Kannai, “Continuity properties of the core of a market”, Econometrica, 38 (1970), 791–815 | DOI | Zbl

[23] H. W. Kuhn, “Some combinatorial lemmas in topology”, IBM J. Res. Develop., 4 (1960), 518–524, MR 23, A1358 | MR | Zbl

[24] H. W. Kuhn, “Simplicial approximation of fixed points”, Proc. Nat. Acad. Sci. U.S.A., 61 (1968), 1238–1242 | DOI | MR | Zbl

[25] C. E. Lemke, J. T. Howson, “Equilibrium points of bimatrix games”, J. Soc. Indust. Appl. Math., 12 (1964), 413–423, MR 30, 3769 | DOI | MR | Zbl

[26] L. W. McKenzie, “On equilibrium in Graham's model of world trade and other competitive systems”, Econometrica, 22 (1954), 147–161 | DOI | Zbl

[27] J. Nash, “Equilibrium points in $n$-person games”, Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 48–49, MR 11, 192 | DOI | MR | Zbl

[28] Review of Economic Studies, 13 (1945), 1–9 | DOI | Zbl

[29] H. Nikaidò, “On the classical multilateral exchange problem”, Metroecon., 8 (1956), 135–145, MR 18, 266 | DOI | MR

[30] H. Scarf, “An analysis of markets with a large number of participants”, Recent Advances in Game Theory, Princeton University Conference Report, 1962

[31] H. Scarf, “The approximation of fixed points of a continuous mapping”, SIAM J. Appl. Math., 5 (1967), 1328–1343, MR 39, 3814 | DOI | MR

[32] H. Scarf, The computation of economic equilibria, Yale Univ. Press, New Haven, Conn., 1973 (with T. Hansen) | MR | Zbl

[33] M. Shubik, “Edgeworth market games”, Contributions to the Theory of Games, vol. IV, Ann. of Math. Studies, 40, Princeton Univ. Press, Princeton, N. J., 1959, MR 21, 2538 | MR

[34] S. Smale, “Global analysis and economics, II A”, J. Math. Economics, 1 (1974), 1–14 | DOI | MR | Zbl

[35] K. Vind, “Edge worth-allocations in an exchange economy with many traders”, Internat. Economic Rev., 5 (1964), 165–177 | DOI | Zbl

[36] A. Wald, “Über die eindeutige positive Lösbarkeit der neuen Produktionsgleichungen”, Ergebnisse eines mathematischen Kolloquiums, 1935, no. 6, 12–20 | Zbl

[37] A. Wald, “Über die Produktionsgleichungen der ökonomischen Wertlehre”, Ergebnisse eines mathematischen Kolloquiums, 1936, no. 7, 1–6 | Zbl

[38] “On some systems of equations of mathematical economics”, Econometrica, 19 (1951), 368–503, MR 13, 370 | DOI | DOI | MR | Zbl

[39] Elements of pure economics, Irwin, Homewood, Ill., 1954

[40] R. J. Wilmuth, The computation of fixed points, Ph. D. Disseration, Stanford University, Stanford, California, 1973