Capitation tax based control of multipopulation replicator dynamics under incomplete information

Many social systems consist of multiple populations of selfish players. In such systems, a problem called a social dilemma may occur. In order to resolve the dilemma, the government tries to control the multiple populations by imposing taxes and offering subsidies to players. Dynamical behaviors of the controlled systems have been discussed by using multipopulation replicator dynamics. Previous work assumed that the taxes and the subsidies of a player depend on which population he/she belongs to. In general, however, the government cannot identify the members of each population. In this paper, we introduce a government that controls multiple populations under such incomplete information, and formulate replicator dynamics. We also derive the stabilization conditions of a target output in the replicator dynamics.