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Existence of Nash Equilibrium in Discontinuous Games

Nessah, Rabia and Tian, Guoqiang (2008): Existence of Nash Equilibrium in Discontinuous Games.

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Abstract

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of continuity, called quasi-weak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. Our conditions are simple and easy to verify. We present applications to show that our conditions allow for economically meaningful payoff discontinuities.

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