Before revision:  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 .
After revision:  In the pure 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 two player finite action game has at least one periodic strategy, making the periodic strategies an inherent characteristic of these games .