成对社会困境博弈的稳定性：破坏性智能体、建设性智能体及其联合效应
Stability of pairwise social dilemma games: destructive agents, constructive agents, and their joint effects
AI总结：
本研究在无限充分混合种群中用复制动力学分析成对社会困境博弈，发现破坏性智能体无法促进合作反而破坏均衡，建设性智能体的效应随收益变化，二者组合会产生多稳态复杂演化动态，深化了对自愿参与机制影响合作的理解。
摘要：
破坏性智能体（选择退出博弈并无差别伤害他人的主体）会反常地促进合作，是自愿参与策略的一个有趣变体。然而，它们对合作的影响仍未得到充分理解，尤其是在成对社会困境博弈的语境下，以及与建设性智能体（选择退出博弈但无差别使他人受益的对应主体）相比时更是如此。此外，人们对两类智能体对合作动态的联合影响也知之甚少。\n我们在无限且充分混合的种群中使用复制动力学展开研究，结果发现：与破坏性智能体在多人博弈中促进合作的作用相反，它们在成对社会困境中无法激励合作。相反，它们会破坏囚徒困境博弈和猎鹿博弈中背叛策略的稳定性，甚至可能取代背叛策略。类似地，在鹰鸽博弈中，它们能破坏合作与背叛混合均衡的稳定性或取代该均衡，并且会削弱和谐博弈中的合作。\n反过来，当建设性智能体的收益超过其对对手的贡献时，会表现出与破坏性智能体相似的效应。但如果它们的收益更低，尽管会破坏囚徒困境和猎鹿博弈中背叛策略的稳定性，却不会扰乱和谐博弈中的合作均衡，且对鹰鸽博弈中合作共存状态的影响可忽略不计。\n破坏性与建设性智能体的组合并不会促进合作，反而会产生复杂的演化动态，包括双稳态、三稳态和四稳态，最终结果取决于它们的相对收益和博弈类型。综合来看，这些结果深化了我们对自愿参与机制影响合作的理解，为更全面认识其作用提供了支撑。
英文摘要：
Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that, contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they destabilize and may even replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, and they undermine cooperation in the harmony game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation but instead generates complex evolutionary dynamics, including bi-stable, tri-stable, and quad-stable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.
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