A control method of selfish routing based on replicator dynamics with capitation tax and subsidy

In social and biological systems, there exist many populations which consist of a large number of selfish players interacting with each other. In such a population, the purpose of each player often conflicts with the total purpose of the population, and a problem such as a social dilemma occurs. To resolve the problem, a government sometimes tries to control the population by imposing a tax on and/or offering a subsidy to each player. As a model of such a situation, replicator dynamics with capitation taxes and subsidies has been proposed. On the other hand, in large computer networks, several inefficiencies due to selfish behaviors of players have been reported. To reduce the inefficiencies, an external agent to control packet flows will be needed and its design methodology is an important issue. In this paper, we apply the control method with capitation taxes and subsidies by the government to a stabilization problem of the minimum latency flow in the selfish routing. We investigate several properties of replicator dynamics which models controlled behaviors by the capitation taxes and the subsidies, and derive some stabilization conditions of the target state. Moreover, we apply the model to Braess graphs and derive a stabilization condition of the minimum latency flow.