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. We prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs.
After revision:  We formally define and study periodic strategies in two player perfect information strategic form games , with pure strategies and we prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs.