Research Of Game Via Semi-tensor Product

Evolutionary game theory is a theory that combines game theory analysis and dynamic evolution analysis.The game contains a considerable number of players involved in the relationship between players and their form a complex network.Players in environment with the mutually competitive relationship,under certain conditions,combined with their own last choice,the environment perception and information in combination with the strategy of updating rules to update their own strategy and achieve a game equilibrium.In this paper,based on the combination of semi-tensor products and Boolean network,the main contents and innovations are as follows:The first chapter,as a preliminary knowledge,introduces the evolutionary network game and Boolean network,the definition and properties of semi-tensor products,and the matrix representation of logic functions.The second chapter,we study strategy optimization in the static game with com-plete based on semi-tensor product.The definition and algebraic expression of the dominant strategy and the dominated strategy is given via STP.Based on some prop-erties of the dominant behaviors,we update the game by deleting some dominated strategies of players,and find the game player’s solution to the static game with com-plete information.An example is given to illustrate the validity of the result.In chapter three,we study the evolutionary network game with different length information based on semi-tensor product.The structure matrix of profit function is used to express the players’ strategies into new variables,and the game is modeled as a linear discrete system with time delay.Finally,we design a state feedback controller to converge the initial state of the whole system to a stable strategy globally,that is to say,the equilibrium of the game is reached.An example is presented to substantiate the effectiveness of the theoretical results.