Analysis And Strategy Optimization Of Games Based On Semi-tensor Product Of Matrices

In this paper,the strategy optimization of coupled public good games,the validation of the weighted potential incomplete-profile games,and the stabilization of Boolean control networks with time delay are investigated by using the semi-tensor product of matrices.The main research contents are listed as follows:1.The strategy optimization of a class of coupled evolutionary public good games with double enhancement factors is studied.The algebraic formulation for the dynamics of the given coupled public good games is constructed by using the semi-tensor product of matrices.Then,the strategy optimization problem is considered based on the algebraic expression.A necessary and sufficient condition is given to detect the total investment of each subgames can reach the threshold,and a constructive algorithm is designed to obtain all the valid state feedback controls.2.The validation and decomposition problem of the weighted potential incomplete-profile games is studied.A weighted potential equation is established by using the semi-tensor product of matrices.And by judging whether the weighted potential equation has a solution,we can detect whether the incomplete-profile game is a weighted potential game or not.The calculation method of the corresponding potential function is given.Then the pure weighted potential subspace and the non-strategic subspace are obtained by decomposing the weighted potential incomplete-profile games.3.The stabilization of Boolean control networks with time delay both in states and inputs is investigated.A necessary and sufficient condition to detect stabilization of BCNs with time delay is obtained.Moreover,a simple algorithm to design all valid state feedback controllers via Ledley antecedence solution is given.