Existence of Equilibrium in Minimax Inequalities, Saddle Points, Fixed Points, and Games without Convexity Sets

Rabia Nessah () and Guoqiang Tian

No 2008-ECO-15, Working Papers from IESEG School of Management

Abstract: This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasi-concavity 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 nonquasiconcave payoff functions and nonconvex and/or noncompact strategy spaces.

Keywords: minimax inequality; saddle points; fixed points; coincidence points; discontinuity; non-quasiconcavity; non-convexity; and non-compactness. (search for similar items in EconPapers)
Pages: 24 pages
Date: 2008-11, Revised 2010-11
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