The Dynamic Game with State Payoff Vector on Connected Graph

By introducing point (state) payoff vector to every point node on connected graph in this paper, dynamic game is researched on finite graph. The concept of strategy about games on graph defined by C. Berge is introduced to prove the existence theorem of absolute equilibrium about games on connected graph with point payoff vector. The complete algorithm and an example in three-dimensional connected mesh-like graph are given in this paper.