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Hilbe, Christian

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Hilbe

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Christian

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Hilbe, Christian
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    Social Dilemmas Among Unequals
    (Springer Science and Business Media LLC, 2019-08) Hilbe, Christian; Hauser, Oliver; Chatterjee, Krishnendu; Nowak, Martin
    Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans and is generally considered to undermine cooperation and welfare. Most previous models of reciprocity do not include inequality. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.
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    A Unified Framework of Direct and Indirect Reciprocity
    (Springer Science and Business Media LLC, 2021-05-13) Schmid, Laura; Chatterjee, Krishnendu; Hilbe, Christian; Nowak, Martin
    Direct and indirect reciprocity are key mechanisms for evolution of cooperation. Direct reciprocity means individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means they also consider the experiences of others. Although the 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 strategy ‘Generous Tit-for-Tat’ of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘Generous Scoring’. With 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. We find that indirect reciprocity evolves if any two individuals meet only occasionally, when information about others is reliable, and when strategy mutations are rare. Our results draw unexpected connections between direct and indirect reciprocity, while highlighting important differences regarding their evolvability.