Fixed points of parameterized perturbations

Andrew McLennan ()

Journal of Mathematical Economics, 2014, vol. 55, issue C, 186-189

Abstract: Let X be a convex subset of a locally convex topological vector space, let U⊂X be open with U¯ compact, let F:U¯→X be an upper semicontinuous convex valued correspondence with no fixed points in U¯∖U, let P be a compact absolute neighborhood retract, and let ρ: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 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).

Keywords: Fixed points; Essential sets; Fixed point index; Homotopy; Kohlberg–Mertens stability; Stochastic games (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Working Paper: Fixed Points of Parameterized Perturbations (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:55:y:2014:i:c:p:186-189

DOI: 10.1016/j.jmateco.2014.07.001

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