Direct reciprocity and model-predictive rationality: A setup for network reciprocity over social ties

Network reciprocity is the simplest mechanism supporting the evolution of cooperation emerging when interactions are localized, rather than all-to-all. It has been recently questioned in social networks, both theoretically and experimentally. Indeed, local interactions favor cooperation when unconditional cooperators play a prisoner's dilemma against unconditional defectors under an imitation process. However, imitation lacks rationality in heterogeneous communities and did not clearly emerge in experiments. What did emerge is a form of conditional cooperation based on direct reciprocity, that is the propensity to cooperate with neighbors who previously showed cooperation. Nonetheless, the beneficial effect of the local interactions seems to be confirmed, whereas what drives strategy update remains unclear. A recent theoretical contribution showed that network reciprocity occurs if conditional cooperators update their strategy rationally optimizing a model-based prediction of future incomes. We here confirm this result, using the classical Tit-for-tat strategy to implement direct reciprocity.