Integrating upstream and downstream reciprocity stabilizes cooperator-defector coexistence in N-player giving games
This study addresses the evolutionary stability of cooperation among strangers in N-person gift-giving games. Method: We propose an integrated reciprocity strategy that jointly incorporates upstream indirect reciprocity (“transmission of kindness”) and downstream indirect reciprocity (“reputation-based reward”), and analyze its dynamics via evolutionary game-theoretic modeling and stability analysis. Results: The strategy enables globally asymptotically stable coexistence of cooperators, defectors, and integrated reciprocators in a three-strategy system; moreover, when the benefit-to-cost ratio satisfies $b/c > 2$, the cooperation frequency remains strictly positive in any finite population. A key contribution is the demonstration that the integration mechanism enhances systemic robustness *retroactively*—i.e., through low-complexity implementation—thereby providing, for the first time at the theoretical level, a viable pathway for sustained cooperation in large-scale anonymous populations.