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　cheat-preventing　was　given.　This　scheme　has　wider　applicability　and　practical　use　as　rational　thinking　has　been　taken　into　consideration.