One step memory of group reputation is optimal to promote cooperation in public goods games

Individuals' change of social ties has been observed to promote cooperation under specific mechanism, such as success-driven or expectation-driven migration. However, there is no clear criterion or information from players' instinctive memory or experience for them to consult as they would like to change their social ties. For the first time we define the reputation of a group based on individual's memory law. A model is proposed, where all players are endowed with the capacity to adjust interaction ambience involved if the reputation of their environment fails to satisfy their expectations. Simulation results show that cooperation decays as the increase of player's memory depth and one step memory is optimal to promote cooperation, which provides a potential interpretation for that most species memorize their reciprocators over very short time scales. Of intrigue is the result that cooperation can be improved greatly at an optimal interval of moderate expectation. Moreover, cooperation can be established and stabilized within a wide range of model parameters even when players choose their new partners randomly under the combination of reputation and group switching mechanisms. Our work validates the fact that individuals' short memory or experience within a multi-players group acts as an effective ingredient to boost cooperation.