  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.
