Abstract
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.
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