Human cooperation persists among strangers in large, well-mixed populations despite theoretical predictions of difficulties, leaving a fundamental evolutionary puzzle. While upstream (pay-it-forward: helping others because you were helped) and downstream (rewarding-reputation: helping those with good reputations) indirect reciprocity have been independently considered as solutions, their joint dynamics in multiplayer contexts remain unexplored. We study public goods games without self-return (often called "others-only" PGGs) with benefit b and cost c and analyze evolutionary dynamics for three strategies: unconditional cooperation (ALLC), unconditional defection (ALLD), and an integrated reciprocity strategy combining unconditional forwarding with reputation-based discrimination. We show that integrating upstream and downstream reciprocity can yield a globally asymptotically stable mixed equilibrium of ALLD and integrated reciprocators when b/c > 2 in the absence of complexity costs. We analytically derive a critical threshold for complexity costs. If cognitive demands exceed this threshold, the stable equilibrium disappears via a saddle-node bifurcation. Otherwise, within the stable regime, complexity costs counterintuitively stabilize the equilibrium by preventing not only ALLC but also alternative conditional strategies from invading. Rather than requiring uniformity, our model reveals one pathway to stable cooperation through strategic diversity. ALLD serves as "evolutionary shields" preventing system collapse while integrated reciprocators flexibly combine open and discriminative responses. This framework demonstrates how pay-it-forward broadcasting and reputation systems can jointly maintain social polymorphism including cooperation despite cognitive limitations and group size challenges, offering a potential evolutionary foundation for behavioral diversity in human societies.

翻译：人类合作在大规模、充分混合的陌生人群体中持续存在，这与理论预测的困境相悖，构成了一个根本性的演化谜题。虽然上游间接互惠（向前传递：因曾被帮助而帮助他人）与下游间接互惠（声誉奖励：帮助声誉良好者）已被独立视为可能的解决方案，但它们在多人情境中的联合动力学机制尚未得到探索。本研究以无自返收益（常称为“他者专属”PGG）的公共物品博弈为框架，设定收益参数b与成本c，分析了三种策略的演化动力学：无条件合作（ALLC）、无条件背叛（ALLD），以及融合无条件传递与基于声誉识别的整合互惠策略。研究表明，当b/c > 2且无认知成本时，整合上游与下游互惠机制可形成ALLD与整合互惠者共存的全局渐近稳定混合均衡。我们通过解析推导得出认知成本的临界阈值：若认知负荷超过该阈值，稳定均衡将通过鞍结分岔消失；反之，在稳定区间内，认知成本会反直觉地通过阻止ALLC及替代性条件策略的入侵来增强均衡稳定性。我们的模型揭示了一条通过策略多样性实现稳定合作的路径，而非要求策略同一性。ALLD扮演着“演化盾牌”的角色防止系统崩溃，而整合互惠策略则灵活结合开放性与识别性响应机制。该框架阐明了向前传递的广播机制与声誉系统如何协同维持包含合作行为的社会多态性，即使面临认知局限与群体规模挑战，为人类社会的行为多样性提供了潜在的演化基础。