Factor Countermeasures And Figure R-countermeasures Research

In this paper, we research the factor method of the game and existence of absolute equilibrium as well as the algorithm of the graph-game with play-payoff. Firstly, on the base of factor-game and assistant-game, we solve the game by the way of decreasing the rank of the game. Then we try to apply it to the prisoners' dilemma and the solving process for rank-game. Finally, we study the graph-game with play-payoff and state-payoff, and prove the existence of absolute equilibrium on the sense of r-strategy as well as the complete algorithm.On the first chapter, we solve the game on the base of constructing the factor-game as well as assistant-game. Comparing the factor-solution with the equilibrium-solution, we explain that players may get better payoffs through the probable "convert" cooperation. Then we define and construct the factor-solution for partial cooperation. The illustration shows that special form of coalition might mean best form of cooperation.On the second chapter, we first describe the process of the rank-game, then study the existence of absolute equilibrium on the non-cooperation situation. For the situation of cooperation, we give the form of character function. Finally, we use factor-game to solve the game according to the character structure of the rank-game.On the third chapter, we try to research the dynamic game on finite connected graph, which players' strategy related to the history, that is the choice for the next point related to the past states, but not the last state that has just past. Focus on the game with play-payoff on connected graph; we prove the existence of absolute equilibrium on the sense of r-strategy. Then we give the complete algorithm of it. If play-payoff is achieved by the method of accumulation of state-payoffs, we prove the lemma of the broken relation of strategy with the history.