Complete study of linear infinite games

In this paper we conduct a sistematic study of linear and ane games. We consider the terms affine and linear in the sense recently introduced by D. Carfì and recalled in the present paper. The study is made in the case in which both the strategy sets of the players are intervals of the real line and when the real bilosses function of the game is a function of class C1. Utterly, in the paper, the case of affine games of this kind is totally solved. The proposed method counts several investigation points, some are classical (Nash equilibria, conservative strategies,...) but many others are totally new and proposed by D. Carfì. The aim of this method is to give an exsaustive and efficient view of the game and of its possible solutions, moreover, the method allows to give a rational judment about the goodness of the diverse solutions of linear and affine games in the non-cooperative and in the cooperative case.