Modeling and Analysis of Networked Evolutionary Games with Weight via Semi-tensor Product Method

This paper studies dynamics behaviors for a class of networked evolutionary games with weight by using semi-tensor product of matrices. Each player is able to choose some of the associated players as their own neighborhoods in weighted networked evolutionary games. Firstly, the model is put forward named networked evolutionary games with weight, which quantify the connections between players. Each player choose their neighborhoods who meet their own mental standards from connected people. Secondly, an algebraic form of the model is got via the semi-tensor product. The dynamical behavior of evolutionary networked games is discussed through it, then some interesting results about attractors are obtained. Finally, an example is showed to illustrate the theoretical results in this paper and explains that the new results can work well.