How Reputation Sustains Cooperation: Mathematical Theories of Indirect Reciprocity

Cooperation among unrelated individuals is a central puzzle in the evolution of social behavior. Indirect reciprocity offers one influential explanation: people help others not only because they expect direct returns, but also because their actions affect their reputation. In this seminar, I will review mathematical theories of indirect reciprocity, focusing on how reputation and social norms can sustain cooperation. I will begin with the classical framework of public assessment, where everyone shares the same view of each individual’s reputation, including the seminal work of Ohtsuki and Iwasa on the “leading eight” social norms. I will then turn to private assessment, where individuals may disagree about others’ reputations, and discuss why synchronization of opinions becomes essential for cooperation. Overall, the seminar aims to provide an accessible overview of how mathematical models allow us to formalize moral judgments—what counts as good or bad behavior—and to understand the evolution of cooperation through reputation.