Abstract: Aiming at the current phenomenon of intergenerational transmission of income inequality, this paper describes and discusses deeply with game theory and mathematical model. From the internal mechanism, it analyzes the intergenerational correlation of the result inequality caused by the unequal opportunities created by the transfer of father's resources and the unequal efforts of the children. The numerical simulation results show that effectively controlling the intergenerational fairness coefficient, improving the return of the offspring's efforts and reducing the intergenerational transfer effect of the father's resources can provide a social institutional environment with an equal opportunity for the economic individual. In addition, combining with the driving force of informal constraints such as social and cultural background on the evolution of the formal system, it can reduce the obstacles to the implementation of the system and truly solve the problem of intergenerational transmission of inequality.

Key words: income inequality; intergenerational transmission; social institutions; cultural background