The co-evolution of direct, indirect and generalized reciprocity

People often engage in costly cooperation, especially in repeated interactions. When deciding whether to cooperate, individuals typically take into account how others have acted in the past. For instance, when one person is deciding whether to cooperate with another, they may consider how they were treated by the other party (direct reciprocity), how the other party treated others (indirect reciprocity), or how they themselves were treated by others in general (generalized reciprocity). Given these different approaches, it is unclear which strategy, or more specifically which mode of reciprocity, individuals will prefer. This study introduces a model where individuals decide how much weight to give each type of information when choosing to cooperate. Through equilibrium analysis, we find that all three modes of reciprocity can be sustained when individuals have sufficiently frequent interactions. However, the existence of such equilibria does not guarantee that individuals will learn to use them. Simulations show that when individuals mainly imitate others, generalized reciprocity often hinders cooperation, leading to defection even under conditions favorable to cooperation. In contrast, when individuals explore new strategies during learning, stable cooperation emerges through direct reciprocity. This study highlights the importance of studying all forms of reciprocity in unison.