Fixed points of parameterized perturbations

McLennan, Andrew (2014) Fixed points of parameterized perturbations. Journal of Mathematical Economics, 55 186-189. doi:10.1016/j.jmateco.2014.07.001

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Author McLennan, Andrew
Title Fixed points of parameterized perturbations
Journal name Journal of Mathematical Economics   Check publisher's open access policy
ISSN 0304-4068
Publication date 2014-12
Year available 2014
Sub-type Article (original research)
DOI 10.1016/j.jmateco.2014.07.001
Open Access Status
Volume 55
Start page 186
End page 189
Total pages 4
Place of publication Amsterdam Netherlands
Publisher Elsevier
Collection year 2015
Language eng
Abstract Let X be a convex subset of a locally convex topological vector space, let U ⊂ X be open with over(U, -) compact, let F : over(U, -) → X be an upper semicontinuous convex valued correspondence with no fixed points in over(U, -) {set minus} U, let P be a compact absolute neighborhood retract, and let ρ : over(U, -) → P be a continuous function. We show that if the fixed point index of F is not zero, then there is a neighborhood V of F in the (suitably topologized) space of upper semicontinuous convex valued correspondences from over(U, -) to X such that for any continuous function g : P → V there is a p ∈ P and a fixed point x of g (p) such that ρ (x) = p. This implies that no normal form game satisfies the conditions specified in Section 4.6 of Levy (2013).
Keyword Fixed points
Essential sets
Fixed point index
Kohlberg-Mertens stability
Stochastic games
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2015 Collection
School of Economics Publications
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
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Created: Tue, 21 Oct 2014, 00:40:55 EST by System User on behalf of School of Economics