Numerous literature shows that gentrification can not only improve the living environment,but also cause some social problems.In the background of consumer utility and developer income,this paper uses the Smith's rent gap theory combined with Nash equilibrium to construct a multi-agent system,and simulates the evolution of gentrification.The results show,firstly,in the assumption of utility maximization,the increase of real income would reduce the probability of gentrification occurrence,leading to narrowing the gap between the rich and the poor.Secondly,in the assumption of profit maximization,the evolution of gentrification depends on the amount of capital invested by developers.However,if it exceeds a threshold value,the extent of gentrification would stop increasing.Thirdly,the evolution of gentrification is associated with the developers' entrance threshold.The higher threshold of developers' entrance implies that developers can make higher returns in the inner-city housing market.As a result,it may raise the sale price of inner-city land to a certain degree and the frequency of gentrification and degentrification.