Strategy Set and Payoff Optimization of a Type of Networked Evolutionary Games

In this paper, we consider the strategy set optimization and payoff optimization for a class of networked evolutionary games (NEGs) with “myopic best response adjustment” by using the semi-tensor product (STP) method, and present a number of new results. Firstly, the dominated strategies are defined, based on which an algorithm for removing dominated strategies is formulated for a given NEG. Secondly, using STP method, the dynamics of the NEG after removing the dominated strategies is converted into an algebraic form. Finally, the payoff optimization problem is considered by adding control players to the game and state feedback controls are designed to steer the game from an initial profile to the optimal profile which can maximize the overall payoff of the whole game. An illustrative example is studied to support our new results.