Study Of Evolutionary Stability Under Different Initial State Of 2×2 Quantum Game Model

Quantum game theory is the use of quantum information theory as a tool to study the game theory,it is an emerging interdisciplinary.More and more get the attention of scholars both at home and abroad in recent years.Evolution stability is also one of the most important basic concepts in the evolution game theory.How to make the two organically,is an important topic which need to be solved at present.Based on this,using the related theory of quantum game theory knowledge,the quantization scheme based on Marinatto and Weber(“MW”),established the symmetric and asymmetric 2×2 quantum game models of two cases,find out the Nash equilibriums and analysis the evolution stability of the model,discuss the different initial state effect on quantum game mode evolution stability.The paper is divided into four chapters.The first chapter introduced in detail the significance of topic selection and research,introduced the research status at home and abroad,pointed out the existing main problems,introduced the theoretical tools and innovations in this paper.The second chapter discusses the different initial states of the effect on the evolution stability of the symmetric quantum game model.The third chapter discusses the different initial states of the effect on the evolution stability of the asymmetric quantum game model.The fourth chapter summarizes the paper conclusion and prospect.Paper main research work is as follows:(1)Based on the “MW” quantization scheme,established under the condition of different initial states 2×2 symmetry quantum game model,get the Nash equilibriums of the model,analysis of the evolution stability of the Nash equilibriums.The influence of the evolutionary stability of the symmetric quantum game model is obtained,and verified by classic examples.(2)Based on the “MW” quantization scheme,established under the condition of different initial states 2×2 asymmetry quantum game model,get the Nash equilibriums of the model,analysis of the evolution stability of the Nash equilibriums.The influence of different initial states on the evolutionary stability of the asymmetric quantum game model is obtained,and verified by classic examples.