Nash equilibria in the noncooperative informational extended games

In this article we will analyse informational extended games, i.e. games in which the players choose their actions simultaneously, with assumption that they have some information about the future strategies which will be chosen by other players. All informational extended games of this type will assume that players' payoff functions are common knowledge. Under these assumptions the last section will define the informational extended games and analyse Nash equilibrium and conditions of its existence. The essential result of this article is a theorem of Nash equilibrium existence in informational extended games with $n$ players. Our treatment is based on a standard fixed point theorem which will be stated without proof in the first section.