Replicator Dynamics with Dynamic Payoff Reallocation Based on the Government's Payoff

Abstract—In a population which consists of a large number of players interacting with each other, the payoff of each player often conflicts with the total payoff of the population which he/she belongs to. In such a situation, the “government” which has the comprehensive perspective is introduced for governing the population. When the government collects and reallocates players’ payoffs for governing the population, the evolutions of population states are modeled by replicator-mutator dynamics. In this paper, we propose a model which describes the evolution of the government’s reallocation strategy and investigate stability of its equilibrium points.