We introduce a new solution concept for selecting optimal strategies instrategic form games which we call periodic strategies and the solution conceptperiodicity. As we will explicitly demonstrate, the periodicity solutionconcept has implications for non-trivial realistic games, which renders thissolution concept very valuable. The most striking application of periodicity isthat in mixed strategy strategic form games, we were able to find solutionsthat result to values for the utility function of each player, that are equalto the Nash equilibrium ones, with the difference that in the Nash strategiesplaying, the payoffs strongly depend on what the opponent plays, while in theperiodic strategies case, the payoffs of each player are completely robustagainst what the opponent plays. We formally define and study periodicstrategies in two player perfect information strategic form games, with purestrategies and generalize the results to include multiplayer games with perfectinformation. We prove that every non-trivial finite game has at least oneperiodic 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 alsoaddress the incomplete information games in the context of Bayesian games, inwhich case generalizations of Bernheim's rationalizability offers us thepossibility to embed the periodicity concept in the Bayesian games framework.Applying the algorithm of periodic strategies in the case where mixedstrategies are used, we find some very interesting outcomes with usefulquantitative features for some classes of games.
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