Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability.
Nature Human Behaviour
This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.), the European Research Council Start Grant 279307: Graph Games (to K.C.), and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
Schmid L, Chatterjee K, Hilbe C, Nowak MA. A unified framework of direct and indirect reciprocity. Nature Human Behaviour. 2021. doi:10.1038/s41562-021-01114-8
Schmid, L., Chatterjee, K., Hilbe, C., & Nowak, M. A. (2021). A unified framework of direct and indirect reciprocity. Nature Human Behaviour. Springer Nature. https://doi.org/10.1038/s41562-021-01114-8
Schmid, Laura, Krishnendu Chatterjee, Christian Hilbe, and Martin A. Nowak. “A Unified Framework of Direct and Indirect Reciprocity.” Nature Human Behaviour. Springer Nature, 2021. https://doi.org/10.1038/s41562-021-01114-8.
L. Schmid, K. Chatterjee, C. Hilbe, and M. A. Nowak, “A unified framework of direct and indirect reciprocity,” Nature Human Behaviour. Springer Nature, 2021.
Schmid L, Chatterjee K, Hilbe C, Nowak MA. 2021. A unified framework of direct and indirect reciprocity. Nature Human Behaviour.
Schmid, Laura, et al. “A Unified Framework of Direct and Indirect Reciprocity.” Nature Human Behaviour, Springer Nature, 2021, doi:10.1038/s41562-021-01114-8.