Abstract: To construct the hierarchical key model which had the extensive game description, a rational threshold signature was raised by combining the dynamic games of complete information in Game Theory.The partial signature of the player could be sent in a certain probability in multi-game process.The probability of the utility which the player had been maximized had been calculated so as to achieve Nash Equilibrium.Extended description of level key module was constructed so that the forged signature could be detected by system PKG.That the signature was reconstructable as deviation was prevented.The security of this scheme was based on the DH problem on group.Feature of correctness and cheatpreventing was given.This scheme has wider applicability and practical use as rational thinking has been taken into consideration.