Externalities, Nonconvexities, and Fixed Points

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[10] Bryant, V. W. (1970) “The Convexity of the Subset Space of a Metric Space”Composito Mathematica 22, 383-385.[11] Carbonell-Nicolau, O. (2010) “Essential Equilibria in Normal-form Games,”Journal of Economic Theory 145, 421-431.[12] Cellina, A. (1969) “Approximation of Set Valued Functions and Fixed PointTheorems,” Annali di Matematica Pura ed Applicata Series IV, LXXXI, 17-24.[13] Chaber, R. and Pol, R. (2005) “On Hereditarily Baire spaces, σ-Fragmentabilityof Mappings and Namioka Property,” Topology and Its Applications 151, 132-143.[14] Charatonik, J. (1964) “Two Invariants Under Continuity and the Incomparabilityof Fans,” Fundamenta Mathematicae 53, 187-204.[15] Charatonik, J., and Charatonik, M. (1998) “Dendrites” Aportaciones MatematicasSerie Comunicaciones 22, 227-253.[16] Crannell, A., Franz, M., and LeMasurier, M. (2005) “Closed Relations andEquivalence Classes of Quasicontinuous Functions,” Real Analysis Exchange 31,409-424.[17] De Blasi, F. S. and Myjak, J. (1986) “On Continuous Approximations for Multifunctions,”Pacific Journal of Mathematics 123, 9-31.[18] Drewnowski, L. and Labuda, I. (1990) “On Minimal Upper SemicontinuousCompact-Valued Maps,” Rocky Mountain Journal of Mathematics 20, 737-752.[19] Duda, R. (1962) “On Convex Metric Spaces III,” Fundamenta Mathematicae 51,23-33.[20] Duda, R. (1969) “On Convex Metric Spaces V,” Fundamenta Mathematicae 68,87-106.[21] Fan, Ky (1961) “A Generalization of Tychonoff’s Fixed Point Theorem,” MathematischeAnnalen 142, 305-310.[22] Fort, M. K. Jr., (1950) “Essential and Nonessential Fixed Points,” AmericanJournal of Mathematics 72, 315-322.[23] Fort, M. K. Jr., (1951-1952) “Points of Continuity of Semicontinuous Functions,”Publicationes Mathematicae Debrecen 2, 100-102.[24] Goodykoontz Jr., J. T. (1974) “Some Functions on Hyperspaces of HereditarilyUnicoherent Continua,” Fundamenta Mathematicae 95, 1-10.[25] Hola, L. (1987) “On Relations Approximated by Continuous Functions,” ActaUniversitatis Carolinae Mathematica et Physica 28, 67-72.58
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Page 5:
cally approximated by continuous fu
Page 12 and 13: the set x 0 x 1 ∈ C w ∗ f(X) is
Page 14 and 15: defined on some probability space,
Page 16 and 17: contains at most one arc (i.e., ¯
Page 18 and 19: into the collection of Ky Fan sets
Page 20 and 21: 3.1 Best Response MappingsLetting p
Page 22 and 23: 4.1 Nikaido-Isoda FunctionsWith eac
Page 24 and 25: Because Φ(z) × Φ(z) is w ∗ ×
Page 26 and 27: where for all n, C n ∈ S E n,then
Page 28 and 29: Definition 4 (The 3M Property - The
Page 30 and 31: Given (48) and the fact that for n
Page 32 and 33: We note that if m(z) ∈ P w ∗ f(
Page 34 and 35: 6.3 AK Convergence of Minimal Nash
Page 36 and 37: and Gr ρZ ×w ∗f ∗ (·) is the
Page 38 and 39: In particular, for all n ≥ N 0 an
Page 40 and 41: the cutting defined by the cut poin
Page 42 and 43: According to our main result, under
Page 44 and 45: By our main approximation result, f
Page 46 and 47: 9 Appendix 1: USCO FundamentalsIn t
Page 48 and 49: 9.3 Equi-QuasicontinuityIn order to
Page 50 and 51: 9.5 Dense SelectionsFor each F ∈
Page 52 and 53: 10 Appendix 2: The Proof of Lemma 8
Page 54 and 55: Noting that if E ∈ D eE ,thenn eE
Page 56 and 57: 12 Appendix 4: The Proof That All K
Page 58 and 59: Letting E 1 =[E 1 \(X × U 2 )] ∪
Page 62: [42] Ward, L. E., Jr. (1958) “A F
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