Abstract: The main contacts of dynamic game analysis theories are sub-game perfect Nash equilibrium analysis,whose key method is backwards induction. Since a long time,it is so confused for academia that the backwards induction is definitely unsuitable with the fact. This paper reveals the origin of backwards induction:first of all,the micro logic is wrong for overall macro logic neglect. In other words,so meo ne focuses on recent interest rather than long interest. Secondly classic multi-stage model of the dynamic game structure cannot fit for the people to consider and balancedly analyze the overall and long interest. This paper constructs a modern structure based on the future dynamic game model and designs the backstepping grey structured algorithm of dynamic multi-stage game,constructs the termination and guide of the multistage dynamic game and offers the convenient and efficient balanced analysis and further explains the paradox of Centipede game.

Key words: Centipede game, grey structured algorithm, the termination and guide of the multi-stage dynamic game