Replicator dynamics with Pigovian subsidy and capitation tax Original Research Article

The selfish behaviors of individuals can cause an inefficient society in which the total amount of the individuals’ utilities is not maximized. To resolve the problem, a government sometimes tries to control the population by imposing a tax on and/or offering a subsidy to the individuals who belong to the population. The tax is roughly classified into rate taxations and capitation taxes. Using an evolutionary game theory, the authors have proposed a differential equation model with rate taxations to analyze their effects on players’ behaviors. In this paper, we propose a differential equation model with the capitation taxes, and derive stability conditions of the target state. Moreover, we also discuss an application of our model to selfish routing games.