Before revision:   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.
After revision:  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 generalize the results to include multiplayer games with perfect information.