Cooperation maintained by fitness adjustment

Questions: Can cooperation be enhanced if players whose performance is higher than the mean are forced to pay an additional cost in each generation? Mathematical methods: Analysis of replicator dynamics with mutation. The ESS distribution of cooperation level is obtained. Key assumptions: Players engage in a cooperative dilemma game, and at the end of each generation those whose performance is higher than the mean are forced to pay an additional cost. Conclusions: Without mutation, the entire population eventually conforms to a single cooperation level determined by the initial composition of the population. With mutation, there is an equilibrium distribution of cooperation, which has a peak at an intermediate level of cooperation. Whether it is institutionalized such as tax or just a social custom, fitness adjustment based ultimately on people's 'envy' is able to maintain cooperation.