Population-independent subsidy and lump-sum tax based control of multipopulation replicator dynamics

Many social systems consist of many selfish players. All players may not have the same sense of values, and players who have different senses of values can be considered to belong different populations. As a model of such systems, multipopulation replicator dynamics has been proposed. In general, the desirable state may not be realized in the systems of many selfish players. In order to realize the desirable state, the government that offers subsidies to players regardless of their populations has been introduced. In previous work, however, it is assumed that there exists an equilibrium point that corresponds to the desirable state. In this paper, in addition to the subsidy, we introduce a lump-sum tax that makes a desirable non-equilibrium target state an equilibrium point and formulate replicator dynamics with the lump-sum tax and the subsidy. We also derive the stabilization conditions of the target state in two-population two-strategy games.