We introduce a new solution concept  for selecting optimal strategies in strategic form games which we call periodic strategies and the solution concept periodicity. As we will explicitly demonstrate, the periodicity solution concept has implications for non-trivial realistic games, which renders this solution concept very valuable. The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find solutions that result to values for the utility function of each player , that are equal to the Nash equilibrium ones , with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays.  We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and generalize the results to include multiplayer games with perfect information. We prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs. In principle the algorithm we provide, holds true for every non-trivial game, because in degenerate games, inconsistencies can occur. In addition, we also address the incomplete information games in the context of Bayesian games, in which case generalizations of Bernheim's rationalizability offers us the possibility to embed the periodicity concept in the Bayesian games framework. Applying the algorithm of periodic strategies in the case where mixed strategies are used, we find some very interesting outcomes with useful quantitative features for some classes of games .
We introduce a new solution concept , called periodicity, for selecting optimal strategies in strategic form games . This periodicity solution concept yields new insight into non-trivial games. In mixed strategy strategic form games, periodic solutions yield values for the utility function of each player that are equal to the Nash equilibrium ones . In contrast to the Nash strategies, here the payoffs of each player are robust against what the opponent plays. Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games with pure strategies and we prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning non-degenerate payoffs. In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available .
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some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available