Reciprocal-reward–based environmental feedback promotes cooperation in spatial prisoner's dilemma game

\n\nReciprocal rewards for cooperative behavior are seen as a way of solving social dilemmas. In fact, reward values should not be fixed, but rather linked to the level of social development. Thus, this work proposes a mechanism by which reciprocal reward values in the spatial prisoner's dilemma game depend on region environmental feedback. Therefore, the reciprocal reward values are non-linear and inversely correlated with the environmental state. Numerical simulations show that the non-linear and dynamic reciprocal reward can significantly improve cooperation compared to the traditional version, which can also reduce social costs to some extent. In addition, a higher level of sensitivity to changes in the environment is beneficial for cooperative evolution. Specifically, while setting reciprocal rewards based on greater local environmental feedback can increase the threshold of temptation b at which cooperators become extinct, its contribution to encouraging cooperation is limited. Furthermore, different interval ranges of b-values will have a corresponding range of local environment to encourage cooperation to achieve the optimum. Finally, the results show that the system has good robustness.\n