At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information
we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.Comment: Comments are welcome. We discretely question the optimality of the Nash equilibrium versus periodic strategies in several contexts of perfect and imperfect information. This paper is a part of our early working paper arXiv:1307.2035v2, which was split in two articles, one published in ACS arXiv:1307.2035v4 and the current paper which is accepted for publication in ACS