  We consider a multiagent system consisting of selfish and heterogeneous
agents. Its behavior is modeled by multipopulation replicator dynamics, where
payoff functions of populations are different from each other. In general,
there exist several equilibrium points in the replicator dynamics. In order to
stabilize a desirable equilibrium point, we introduce a controller called a
government which controls the behaviors of agents by offering them subsidies.
In previous work, it is assumed that the government determines the subsidies
based on the populations the agents belong to. In general, however, the
government cannot identify the members of each population. In this paper, we
assume that the government observes the action of each agent and determines the
subsidies based on the observed action profile. Then, we model the controlled
behaviors of the agents using replicator dynamics with feedback. We derive a
stabilization condition of the target equilibrium point in the replicator
dynamics.
