The Other Side of the Coin: Recipient Norms and Their Impact on Indirect Reciprocity and Cooperation

Human cooperation depends on indirect reciprocity. In this work, we explore the concept of indirect reciprocity using a donation game in an infinitely large population. In particular, we examine how updating the reputations of recipients influences cooperation. Our work adds a time-scale parameter for updating donor and recipient reputations. We find a trade-off between the level of cooperation and evolutionary stability influenced by social norms. `Forgiving' recipient norms enhance cooperation but increase susceptibility to defectors, whereas `unforgiving' norms reduce cooperation but defend against invasion by defectors. Expanding to include gossip groups allows us to analyze the evolutionary dynamics of the time-scale parameter, identifying `generous' norms that support cooperation, and `strict' norms that discourage such generosity, ultimately showing vulnerability to defector invasions and potential cooperation collapse.