Asymptotically stable equilibrium and limit cycles in the Rock-Paper-Scissors game in a population of players with complex personalities

► We discuss the Rock-Paper-Scissors (RPS) game in which the fitness of the strategy depends on its frequency. ► We find an asymptotically stable polymorphism in the standard RPS game. ► For the general RPS game we find limit cycles. ► The stability of the limit cycles depends on the personality of the players. ► Supercritical and subcritical Hopf bifurcations are discussed.