Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with “myopic best response adjustment” rule, and presents a number of new results. First, the dynamics of the evolutionary networked game is converted to an algebraic form via the semi-tensor product, and an algorithm is established to construct the algebraic formulation for the game. Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented. Finally, the strategy optimization problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to maximize the average payoff of the pseudo-player. The study of an illustrative example shows that the new results obtained in this paper work very well.