# On the existence of Nash equilibrium in discontinuous games

Research Article

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## Abstract

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of very weak 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. We present applications to show that our conditions allow for economically meaningful payoff discontinuities.

## Keywords

Discontinuous games Quasi-weak transfer continuity Various notions of transfer continuity Nash equilibrium## JEL Classification

C72 C62## References

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