Some extensions of discrete fixed point theorems and their applications to the game theory

As is well‐known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure‐strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non‐cooperative games.