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Periodic Strategies a New Solution Concept-Algorithm for non-trivial Strategic Form Games

By V. K. Oikonomou, V. K. Oikonomou and J. Jost

Abstract

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 dif-ference 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. I

Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.1016.325
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