Note on Pure-strategy Nash equilibria in matrix games

摘要

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.