Keeping or reversing social norms promote cooperation by enhancing indirect reciprocity

Indirect reciprocity facilitates cooperation in social dilemmas by assessing the behaviors of agents through social norms. In this paper, we introduce two new types of second-order social norms with keeping rule and reversing rule, respectively. Besides, this paper also considers two different reputation scenarios, namely, public and private reputation scenarios. To verify the impact of social norms with keeping or reversing rules on cooperation, we develop an evolutionary theoretical model. Through numerical multi-agent simulations, we find that social norms with keeping or reversing are conducive to cooperation. Specifically, for the low benefit-cost ratio, the keeping rule can encourage cooperation, while for the high benefit-cost ratio, the reversing rule can promote cooperation. In addition, simulation results also suggest that the influences of the two reputation scenarios on the evolution of cooperation are different. The public reputation scenario provides a more favorable environment for cooperation than the private reputation scenario. Moreover, we observe that the increase of system noise level, whether action error or mutation rate, will have negative impacts on the emergence of cooperation.