# NOTE ON PURE-STRATEGY NASH EQUILIBRIA IN MATRIX GAMES

• Ma, Weidong (Institute of Applied Mathematics AMSS Chinese Academy of Sciences)
• Published : 2012.11.30

#### Abstract

Pure-strategy Nash Equilibrium (NE) is one of the most important concepts in game theory. Tae-Hwan Yoon and O-Hun Kwon gave a "sufficient condition" for the existence of pure-strategy NEs in matrix games [5]. They also claimed that the condition was necessary for the existence of pure-strategy NEs in undominated matrix games. In this short note, we show that these claims are not true by giving two examples.

#### References

1. D. Fudenberg and J. Tirole, Game Theory, The MIT Press, 1992.
2. J. Nash, Non-cooperative games, Ann. of Math. (2) 54 (1951), 289-295.
3. G. Owen, Game Theory, Academic Press, 1982.
4. J. H. Wang, The Theory of Games, TsingHua University Press, 1988.
5. T. Yoon and O. Kwon, On pure-strategy equilibria in matrix games, Bull. Korean Math. Soc. 37 (2000), no. 2, 377-385.