The Study On Algorithm Of Multi-objective Game Equilibrium Solution

As a branch of mathematics, multi-objective game has a wide range of application in biology, economic, computer science, military strategy and other fields. Therefore, it is significant to study the multi-objective game. In view of this, this paper mainly studies the existence of the equilibrium solution and solution algorithm of the static and dynamic about the complete information of the multi-objective game.Firstly, this paper demonstrated the existence of equilibrium solution in the balanced coordination sense of the static and dynamic about the complete information of the multi-objective game system. This paper demonstrated the existence of equilibrium solution in the equilibrium coordination sense of game system based on the studied of the existence of the equilibrium coordination optimal value of each player’s payment function, for the plurality players and multiple payment function problem of the multi-objective game. The study laid a theoretical foundation for balanced coordination algorithm of multi-objective game proposed.Secondly, the equilibrium coordination algorithm has been proposed about the static multi-objective game problem with complete information. Each player’s expected is adjusted according to the principle of “balanced coordinated” in this algorithm, until obtain lexicographical equilibrium of the game system. The algorithm is applied to the game problem of three oligarchs companies for production competing, and it tests the rationality and validity of the algorithm.Then, this paper established the model of dynamic multi-objective game with complete information. For stackelberg game of the plurality players and multiple payment function, there are such four models have been established respectively as non-cooperative multi-objective stackelberg game model, multi-objective stackelberg game model that the first action cooperate, multi-objective stackelberg game model that the last action cooperate, and multi-objective stackelberg game model that the first action and the last action cooperate respectively.Finally, the paper provides the solution algorithm for multi-objective stackelberg game problem. This paper proposing four kinds of solution algorithm based on the criteria of minimax decision to the four kinds of model for the multi-objective stackelberg game. The algorithm is applied to the game problem of five oligarchs companies for price competing, and it tests the rationality and validity of the algorithm.