Tolerant integrated reciprocity sustains cooperation in a noisy environment.

Human cooperation relies on both direct and indirect reciprocity. While these mechanisms are often treated as separate, real-world decision-making frequently involves integrating the two. However, the existing literature has paid limited attention to the contextual factors and mechanisms supporting the coexistence of direct and indirect reciprocity. This study proposes and analyses a model of integrated reciprocity that combines personal experiences with reputational information. Using agent-based simulations, we systematically and comprehensively evaluate social norms and demonstrate that tolerant integrated reciprocity, which incorporates a partner's past behaviour and reputation, can sustain cooperation more robustly than strategies based solely on direct or indirect reciprocity. In particular, the combination of tolerant integrated reciprocity with the "Standing" norm maintains high cooperation levels even in noisy environments characterised by assessment and implementation errors. These findings suggest that tolerance and using multiple information sources provide an adaptive advantage in sustaining cooperation.