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2010•Unpublished venueRequires access

ON THE EXISTENCE OF NASH EQUILIBRIUM POINTS IN LARGE GAMES

PU Yong-jian

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Abstract

In this paper,noncooperative game with an infinite number of players is considered. By generalizing section theorem,we show that 1) there exists one Nash equilibrium point in large games at least;2) there exists a mixed strategy Nash equilibrium point in continuous large game such that pure strategy sets are nonempty compact metric space and payoff functions are continuous.The results can imply the existence theorem of Salonen in 2010.

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In this paper,noncooperative game with an infinite number of players is considered. By generalizing section theorem,we show that 1) there exists one Nash equilibrium point in large games at least;2) there exists a mixed strategy Nash equilibrium point in continuous large game such that pure strategy sets are nonempty compact metric space and payoff functions are continuous.The results can imply the existence theorem of Salonen in 2010.

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Available abstract

In this paper,noncooperative game with an infinite number of players is considered. By generalizing section theorem,we show that 1) there exists one Nash equilibrium point in large games at least;2) there exists a mixed strategy Nash equilibrium point in continuous large game such that pure strategy sets are nonempty compact metric space and payoff functions are continuous.The results can imply the existence theorem of Salonen in 2010.

Key concepts: Nash equilibrium, Mathematical economics, Mathematics, Epsilon-equilibrium, Best response, Symmetric equilibrium, Risk dominance, Folk theorem

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