Indexed on: 23 Nov '14Published on: 23 Nov '14Published in: Computer Science - Computer Science and Game Theory
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.