| This paper studies how marital bliss is promoted by adjusting the social relationships within the same sex with the help of evolutionary game theory.Marital bliss is one of the ideal paradigms for parental care,in which males contribute in raising offspring and females require a courtship time.Yet marital bliss state is neither Nash equilibrium nor Pareto optimum for the classic Battle of the Sexes.Therefore,it is an ecological puzzle to explain the emergence of marital bliss under natural selection.Previous works concentrate on the pairwise interactions between the two sexes to fill this gap,such as the courtship time and encounter rate.However,whether in the animal world or in human society,same-sex social relationships are important for the development of whole species,and the effect of same-sex social relationships on marital bliss has not been studied.Therefore,we study strategies and co-evolutionary dynamics on social networks to uncover the dynamics that promote marital bliss.The difficulties of dynamic analysis in this paper are as follows:1.The model is both multi-scale and double-random,and the dynamics is based on two populations,with both strategy evolution and network evolution occurring in each population;2.The complexity of imitation rules is high and the conclusion is robust.To solve the first problem,based on the separation principle of time scale,the speed of individual adjustment of social relations is much faster than the speed of strategy update,and a twodimensional differential dynamic system is established.Rigorous deterministic dynamics analysis found that a set of symmetric games emerged through the adjustment of social relations within the sexes.The evolutionary outcome is determined by the interaction between emergent symmetric game and gender war game.When males are rational(i.e.strong selection intensity)and females are irrational(i.e.weak selection intensity),marital bliss can emerge.Maintaining close social relationships between Coy females not only stabilizes marital happiness but also accelerates its convergence.In order to solve the second problem,through dynamic analysis,this paper gives the general criterion that any imitation function can promote the stability of marital bliss,and verifies it by Monte Carlo simulation.Our work reveals a general dynamic analysis method for asymmetric games on dynamic networks,and based on this method we find a pattern of same-sex social relationship adjustment that promotes marital bliss.According to the context of the research,this paper is divided into the following chapters:The first chapter is the introduction.In this chapter,we will focus on the research background,including the biological background,and the model we used--Battle of the Sexes game.It also introduces the current research status,the previous research direction and research conclusions on the issue of promoting marital bliss.This leads us to the object of our study:the adjustment of social relationships within the same sex.The second chapter introduces the relevant knowledge of game theory.For example,Nash equilibrium and evolutionarily stable strategy are defined,and four equilibria in replication dynamics are introduced.The third chapter is the research model.We introduce the mating patterns and income sources of male and female populations and the specific evolutionary rules of strategy updating and linking dynamics.The fourth chapter gives the theoretical analysis results of what kind of social relationship within the same sex can promote marital bliss,and analyzes according to different selection intensity.We also give the criterion that can accelerate the realization of marital bliss,and finally prove the robustness of the above conclusions.The fifth chapter is the summary of our above work and the expectation of future work based on this work. |
