Weakly continuous security and nash equilibrium

Rabia Nessah ()
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Rabia Nessah: IESEG School of Management, Univ. Lille, CNRS, UMR-9221, LEM-Lille Economie Management

Theory and Decision, 2022, vol. 93, issue 4, No 6, 725-745

Abstract: Abstract This paper investigates the existence of pure strategy Nash equilibria in discontinuous and nonquasiconcave games. We introduce a new notion of continuity, called weakly continuous security, which is weaker than the most known weak notions of continuity, including the surrogate point secure of SSYM game of Carbonell-Nicolau and Mclean (Econ Theory, 2018a), the continuous security of Barelli and Meneghel (Econometrica 81:813–824, 2013), C-security of McLennan et al. (Econometrica 79:1643–1664 2011), generalized weakly transfer continuity of Nessah (Economics 47:659–662, 2011), generalized better-reply security of Carmona (Econ Theory 48:1–4, 2011), Barelli and Soza (On the existence of Nash equilibria in discontinuous and qualitative games, 2009), Barelli and Meneghel (Econometrica 81:813–824, 2013), lower single deviation property of Reny (Further results on the existence of Nash equilibria in discontinuous games. University of Chicago, 2009), better-reply security of Reny (Econometrica 67:1029–1056, 1999) and the results of Prokopovych (Econ Theory 48:5–16, 2011, Econ Theory 53:383–402, 2013) and Carmona (J Econ Theory 144:1333–1340, 2009). We show that a compact, convex and weakly continuous secure Hausdorff locally convex topological vector space game has a pure strategy Nash equilibrium. Moreover, it holds in a large class of discontinuous games.

Keywords: Discontinuous games; Nonquasiconcave games; Pure strategy Nash equilibrium; Weakly continuous security; Pseudo upper semicontinuity; Generalized payoff security; Weakly reciprocal upper semicontinuity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11238-022-09869-w

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