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Intersecting Families of Sets and the Topology of Cones in Economics
Author(s):
G.
Chichilnisky
Journal:
Bull. Amer. Math. Soc.
29
(1993),
189-207.
MSC (2000):
Primary 55N10, 90A14, 90A08
MathSciNet review:
1218037
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References:
- *
- {alexandroff} P. Alexandroff and H. Hopf, {\em Topologie},Chelsea Publishing Co. Bronx, New York, 1965. MR 185557
- *
- {arrow} K. J. Arrow, {\em An extension of basic theorems ofclassical welfare economics}, {Proceedings of theSecond Berkeley Symposium on Mathematical Statistics and Probability}(J. Neyman, ed.), Univ. of California Press, Berkeley, CA, 1951, pp. 507--532. MR 44815
- *
- {arrowdebreu} K. Arrow and G. Debreu, {\em Existence of anequilibrium for a competitive economy}, {Econometrica} {\bf 22} (1954), 264--290. MR 77069
- *
- {arrowhahn} K. Arrow and F. Hahn, {\em General competitiveanalysis,} North-Holland, Amsterdam, New York, Oxford, and Tokyo, 1971 (fourthprinting: 1986). MR
- *
- {arrow2} K. J. Arrow, {\em Social choice and individualvalues}, Cowles Foundation Monographs, Wiley, New York, 1953. MR
- *
- {berge} C. Berge, {\em Topological spaces}, Oliver and Boyd,Edinburgh and London, 1963. MR
- *
- {cartan} H. Cartan, {\em Un theorem de finitude}, %{Seminaire Cartan}, Expose 17, 1954. MR
- *
- {chichilnisky} G. Chichilnisky, {\em Social choice and thetopology of spaces of preferences}, {Adv. Math.} {\bf 37} (1980), 165--166. MR 591725
- *
- {chichilnisky10} \bysame, {\em Intersecting families ofsets}\,: {\em a topological characterization}, Working Paper no. 166, Univ. of Essex, February 1981. MR
- *
- {Chichilnisky2aa} \bysame, {\em The topologicalequivalence between the Pareto condition and the existence of dictators}, {J. Math. Econom.} {\bf 9} (1982), 223--233. MR 645650
- *
- {Chichilnisky2} \bysame, {\em Topology and economics}\,:{\em the contribution of Stephen Smale}, { From Topology to Computation}, Proceedings of the Smalefest (M. Hirsch, J. Marsden, and M. Shub, eds.), Springer-Verlag, New York, 1993. MR 1246102
- *
- {Chichilnisky4} \bysame, {\em Limited arbitrage isnecessary and sufficient for the existence of a competitive equilibrium}, Working Paper, Columbia Univ., 1992. MR
- *
- {chichilnisky3} \bysame, {\em Markets, arbitrage andsocial choice}, Working Paper, Columbia Univ., 1991. MR
- *
- {Chichilnisky5} \bysame, {\em On strategic control},{Quart. J. Econom.}, February 1993, 285--290. MR
- *
- {chichilniskyheal} G. Chichilnisky and G. M. Heal, {\em Necessary and sufficient conditions for a resolution of the social choiceparadox}, {J. Econom. Theory} {\bf 31} (1983), 68--87. MR 720115
- *
- {Chichilnisky6} \bysame, {\em Patternsof power}, {J. Public Econom.} {\bf 23} (1984), 333--349. MR
- *
- {chichilnisky7} \bysame, {\em Existence ofa competitive equilibrium in Sobolev spaces, without bounds on shortsales}, {J. Econom. Theory} {\bf 59} (1993), 364--384. MR
- *
- {Chichilnisky11} G. Chichilnisky, {\em Market cones and theglobal convergence of a process of price adjustment}, Working Paper,Columbia Univ., 1993. MR
- *
- {danzer} L. Danzer, V. Klee, and B. Grunbaum, {\em Helly\,\RM'sTheorem and its relatives}, {Proc. Sympos. PureMath.}, vol. VII, Amer. Math. Soc., Providence, RI, 1963. MR 157289
- *
- {choquet} G. Choquet, {\em Lectures on analysis, Volume} II,{Representation Theory}, (J. Marsden, T. Lance, and S. Gerlbart, eds.),W. A. Benjamin, New York and Amsterdam, 1969. MR 250012
- *
- {debreu} G. Debreu, {\em Smooth preferences}, {Econometrica%} {\bf 40} (1971), 603--615. MR 334875
- *
- {dowker} C. H. Dowker, {\em Lectures on sheaf theory}, TataInstitute of Fundamental Research, Bombay, 1957. MR 87097
- *
- {eaves} C. Eaves, {\em Homotopies for computation of fixedpoints}, {Math. Programming} {\bf 3} (1972). MR
- *
- {eggleston} H. G. Eggleston, {\em Convexity}, Cambridge Tractsin Math. Math. Phys., {\bf 47}, Cambridge Univ. Press, Cambridge and New York,1958. MR 124813
- *
- {guesnerie} R. Guesnerie and C. Oudu, {\em On economic gameswhich are not necessarily superadditive}, {Econom. Lett.} (1979). MR
- *
- {heal} G. Heal, {\em Contractibility and public decisionmaking}, {Social Choice and Welfare} (P. Pattanaik and M.Salles, eds.), chapter 7, North-Holland, Amsterdam, 1983. MR 717794
- *
- {helly} E. Helly, {\em Uber Mengen Konvexen Korper mitGemeinschaftlichen Punkten}, {Jber. Deutch. Math. Verein} {\bf 32} (1933), 175--186. MR
- *
- {helly2} \bysame, {\em Uber Systeme Abgeschossener Mengen mitGemeinschlaftlichen Punkten}, {Monatsch. Math}. {\bf 37} (1930), 281--302. MR
- *
- {hirsch} M. Hirsch, {\em A proof of the non-retractability of acell onto its boundary}, {Proc. Amer. Math. Soc.}{\bf 14} (1963), 364--365. MR 145502
- *
- {hirsch2} M. Hirsch and S. Smale, {\em On algorithms forsolving $f(x)=0$}, {Comm. Pure Appl. Math.} {\bf 32} (1979), 281--312. MR 517937
- *
- {leray} J. Leray, {\em Sur la forme des espaces topologiques,et sur les point fixes des representations}, {J. Math. Pures Appl.} (9) {\bf 24} (1945), 95--248. MR 15786
- *
- {nash} J. F. Nash, {\em Equilibrium points in $n$-persongames}, {Proc. Nat. Acad. Sci.} U.S.A. {\bf 36} (1950), 48--49. MR 31701
- *
- {scarf} H. Scarf, {\em The core of an n-person game}, {%Econometrica} {\bf 35} (1967), 50--69. MR 234735
- *
- {smale} S. Smale, {\em Exchange processes with priceadjustment}, {J. Math. Econom.} {\bf 3} (1976), 211--226. MR 452565
- *
- {smale2} \bysame, {\em A convergent process of price adjustmentand global Newton method}, {J. Math. Econom.} {\bf 3} (1976),107--120. MR 411577
- *
- {spanier} E. H. Spanier, {\em Algebraic topology}, Springer-Verlag, New York, Heidelberg, and Berlin, 1966. MR 210112
- *
- {vonneumann} J. Von Neumann, {\em A model of general economicequilibrium} (G. Morgenstern, transl.), {Review Econom. Stud.%} {\bf XIII} (1945--1946), 1--9. MR
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00439-7
PII:
S 0273-0979(1993)00439-7
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