How cooperation arises from rational players?

How to achieve cooperation from rational players is a fundamental problem in various aspects of social and economic systems. In this paper, we present a direct and neat way to lead to cooperation in a dynamical Prisoners´ Dilemma game. In our scenario, the two players are heterogenous and play different roles as the `leader´ and the `follower´ respectively. When the leader is restricted to take the 1-step-memory strategy, it is proved that both the leader and the follower will co-evolve into and stay at the cooperation state (C;C), and the equilibrium strategy turns out to be (Tit f or Tat, ALL C). In this dynamic Stackelberg-alike game, the heterogeneity of the players´ roles and the multi time-scales to improve their strategies are important for cooperation. Related questions for general cases are also investigated.