We define and study periodic strategies in two player finite strategic form games . This concept can arise from some epistemic analysis of the rationalizability concept of Bernheim and Pearce. We analyze in detail the pure strategies and mixed strategies cases. In the pure strategies case, we prove that every two player finite action game has at least one periodic strategy, making the periodic strategies an inherent characteristic of these games . 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. Particularly interesting are the implications of the algorithm to collective action games, for which we were able to establish the result that the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue for the case the players have a continuum set of strategies available. We also discuss whether periodic strategies can imply any sort of cooperativity. In addition, we put the periodic strategies in an epistemic framework .
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 strategies playing, 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 support all our results throughout the article by providing some illustrative examples .
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define and study periodic strategies in two player finite
introduce a new solution concept for selecting optimal strategies in
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. This concept can arise from some epistemic analysis of
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
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rationalizability concept of Bernheim and Pearce. We analyze in detail the pure strategies and mixed strategies cases. In the pure
Nash strategies playing, the payoffs strongly depend on what the opponent plays, while in the periodic
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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
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two player finite action
non-trivial finite
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making the periodic strategies an inherent characteristic of these games
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
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Particularly interesting are the implications of the algorithm to collective action games, for which we were able to establish the result that the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue for the case the players have a continuum set of strategies available. We also discuss whether periodic strategies can imply any sort of cooperativity. In addition, we put the periodic strategies in an epistemic framework
We support all our results throughout the article by providing some illustrative examples