A model of local and global reciprocity

Abstract

We often decide how to treat friends based on observations of their past behavior, whereas actions toward strangers are typically guided by their public reputations. These two kinds of information underlie two classical mechanisms for the evolution of cooperation$\unicode{x2014}$direct and indirect reciprocity$\unicode{x2014}$which have largely been studied in isolation. They are not interchangeable: we can recall the past actions of only a small circle of close contacts, whereas for the far larger pool of strangers we must rely on public reputations. Here we develop a mathematical framework built on this distinction. Each individual engages in direct reciprocity in local games within a finite neighborhood of friends, whose actions they observe directly, and in indirect reciprocity in global games with a large population of strangers, known only by reputation. Separating local and global interactions allows us to address two questions. First, can cooperation persist under a cognitively simple norm of judgment? We show that combining direct and indirect reciprocity resolves the scoring dilemma: conditional cooperators resist invasion by both unconditional cooperators and unconditional defectors, where indirect reciprocity alone would fail. Second, how should one treat a friend whose past behavior conflicts with their public reputation? We find that the strategies that maximize cooperation are forgiving$\unicode{x2014}$overlooking whichever piece of information is unfavorable$\unicode{x2014}$and that these forgiving strategies can often remain robust to invasion. By distinguishing between local and global scales of interaction and integrating information across them, our framework offers a more cognitively realistic account of how reciprocity sustains cooperation.