Modeling and Analysis for A Class of Networked Evolutionary Games with Finite Memories via Semi-tensor Product Method

In many practical problems, players' strategies in the last finite steps are regarded as public information, based on which players decide their strategies at next moment. Considering the individual difference in players, the number of each player's public strategy steps may be different. Thus, this article investigates the modeling and analysis of a class of networked evolutionary games with finite memories by using the semi-tensor product of matrices. Firstly, the model for this class of networked evolutionary games with finite memories is given and a class of myopic best response adjustment rule for the model is designed. Secondly, the algebraic form of the model is given via the semi-tensor product. Thirdly, an algorithm for constructing the corresponding structural matrix is got, then the dynamical behaviors of the model can be analyzed. At last, an illustrative example is given to show the theoretical results in this paper and the effectiveness of the model.