Reward depending on public funds stimulates cooperation in spatial prisoner's dilemma games

Prisoner's dilemma (shortly, PD) games are studied on a square lattice, in which reward mechanisms are considered to stimulate cooperation. It is known to all that results vary with different reward methods. The tax mechanism, an effective tool to adjust the economy, inspires a reward approach where each player should pay corresponding taxes according to their payoff ranks to gather public funds, which is utilized to reward cooperators. There are three main reward levels: high intensity, middle intensity and low intensity. When total public funds keep relatively stable, the reward coverage is determined by the reward intensity. In other words, high intensity of reward is accompanied with narrow range and low intensity accompanies with wide range. Through the proposed model, whether the new reward mechanism can stimulate cooperation and what reward level is the optimum choice could be studied. Simulations reveal that this new mechanism is of great benefit to cooperation and it is noteworthy that low reward intensity with wide coverage has the biggest impact on cooperation.