Cooperation under institutional incentives with perfect and imperfect observation

Understanding the evolution of cooperation is a challenging topic in various realms. Increasing attention has been paid to exploring the effects of incentives on the emergence of cooperation. Most of the extant studies have implicitly assumed that the cost of incentives is fixed and independent of the individual's payoff. In human societies, taxation is one important source of funds for supporting the government of individuals and nearly involves everyone. Inspired by this phenomenon, we institute an analytic model where the incentives are established based on the tax regime. Individuals play the prisoner's dilemma game and the ones whose payoffs are greater than zero have to contribute a part as taxes to establish an institution to monitor individuals' behaviors and execute incentives. We investigate the emergence of cooperation under the institutional incentives and make a comparative analysis between reward and punishment subject to the perfect and imperfect environment.