Model And Simulation Research On Netwokded Evolutionary Games

In nature and human society, cooperative behavior is widespread. But froman evolutionary point of view, collaborators to help others at the same time tendto reduce their chance of survival, and thus at a disadva ntage in natural selection.How to understand the generation and maintenance of cooperative behavioramong selfish individuals is the concern. The evolutionary game theory to studysuch issues provides a powerful tool. Meanwhile, as a new kind of multiplication,semi-tensor product gets more and more attention and participation. It alsoprovides a new method to solve the problem of networked evolutionary games.This paper uses the powerful tool of semi-tensor product to study its applicationin networked evolutionary games. And some common classic examples are givenand analysed. The main contents are as follows.Firstly, we make a brief introduction about the definition of the semi-tensorproduct.Then we briefly summarize some common classic games and theirrelated models, including Prisoner’s Dile mma Game and Snowshift Game. Bymeans of the tool of semi-tensor product, we found the mathematical model ofnetworked evolutionary games and analyze its algebraic structure.Secondly, we give the evolutionary game model under homogeneousnetworks. Different from non-homogeneous networks, we can computehomogeneous networks’s algebraic structure more easily. For the prisoner’sdilemma model as we known, we research the effect of income parameters on thewhole evolutionary process, and obtain some general results.Finally, the paper gives a brief description about the control problem ofnetworked evolutionary games. We give a classic example and analysis itscontrol effect. Meanwhile, the paper studies the problem of multi-speciesevolutionary game on networks. We conduct a preliminary study by using theexample of Hawk-dove Game.