发表机构
Faculty of Economics, Sophia University（上智大学经济学部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在囚徒困境中引入社会偏好，发现合作取决于对对手利他性的信念及信心，而非利他本身，且该信念驱动的合作是脆弱的，仅在信心超过阈值时成立。
AI 中文摘要
我们研究了囚徒困境（PD）中的合作机制。将社会偏好作为效率关切纳入囚徒困境博弈，我们探讨了利他主义如何转化为合作。在完全信息下，合作要求对手的利他程度超过一个阈值。随后，我们引入了贝叶斯纳什均衡的主观扩展，该扩展放宽了共同先验假设，允许参与人对彼此的利他类型持有异质的、可能被错误设定的信念。此时，合作取决于关于利他主义的信念而非利他主义本身，并且即使对手平均仅具有弱利他性，合作也能得以维持。当对剥削的恐惧主导了背叛的诱惑时，关于对手合作的信念成为战略互补品，因此在相同的收益和相同的、正确设定的先验下，合作均衡与不合作均衡可以共存。利用乘子偏好，我们随后研究了这种由信念驱动的合作对模型误设的稳健性。合作是脆弱的：它仅在对自己信念的信心超过某一阈值时才能存续，并且即使信念本身正确支持合作，合作也可能瓦解。作为形式上的扩展，将相同的稳健控制工具应用于参与人的行动选择，可将纳什均衡、贝叶斯纳什均衡和logit分位数响应均衡作为极限情形包含其中。合作更多地取决于参与人相互之间的信念，以及他们对自己信念正确性的信心，而非参与人自身的利他程度。
英文摘要
We study a mechanism of cooperation in the Prisoner's Dilemma (PD). Incorporating social preferences as efficiency concerns into the PD game, we study how altruism translates into cooperation. Under complete information, cooperation requires the opponent's altruism to clear a threshold. We then introduce a subjective extension of Bayesian Nash equilibrium that relaxes the Common Prior Assumption, letting players hold heterogeneous, potentially misspecified beliefs about each other's altruistic type. Cooperation then depends on beliefs about altruism rather than altruism itself, and can be sustained even when opponents are, on average, only weakly altruistic. When fear of exploitation dominates the temptation to defect, beliefs about the opponent's cooperation become strategic complements, so a cooperative and an uncooperative equilibrium can coexist under identical payoffs and an identical, correctly specified prior. Using multiplier preferences, we then study how robust this belief-driven cooperation is to model misspecification. Cooperation is fragile: it survives only above a threshold level of confidence in one's own belief, and can unravel even when the belief itself correctly supports cooperation. As a formal extension, the same robust-control apparatus, applied to a player's action choice, nests Nash equilibrium, Bayesian Nash equilibrium, and logit Quantal Response Equilibrium as limiting cases. Cooperation depends less on how altruistic agents are than on what they believe about each other, and how confident they are that this belief is right.
