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


  • 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. 2012 Springer Science+Business Media, LLC.

published proceedings

  • Journal of Optimization Theory and Applications

author list (cited authors)

  • Nessah, R., & Tian, G.

citation count

  • 19

complete list of authors

  • Nessah, Rabia||Tian, Guoqiang

publication date

  • April 2013