Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions

Rabia Nessah () and Guoqiang Tian
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Rabia Nessah: CNRS-LEM (UMR 8179)

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 1, No 5, 75-95

Abstract: Abstract This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasiconcavity of functions and convexity or compactness of choice sets. A new condition, called “local dominatedness property”, is shown to be necessary and further, under some mild continuity condition, sufficient for the existence of equilibrium. We then apply the basic result obtained in the paper to generalize the existing theorems on the existence of saddle points, fixed points, and coincidence points without convexity or compactness assumptions. As an application, we also characterize the existence of pure strategy Nash equilibrium in games with discontinuous and non-quasiconcave payoff functions and nonconvex and/or noncompact strategy spaces.

Keywords: Minimax inequality; Saddle points; Fixed points; Coincidence points; Discontinuity; Non-quasiconcavity; Non-convexity; Non-compactness (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (11)

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Working Paper: Existence of solution of minimax inequalities, equilibria in games and fixed points without convexity and compactness assumptions (2013)
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DOI: 10.1007/s10957-012-0176-5

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