We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here, we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”

中文翻译：

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大社会的记录保存与合作

我们引入了一种在大量人群中重复游戏的新模型，该模型具有随机匹配、世代重叠和过去游戏的有限记录。我们证明在记录的一般条件下存在稳态均衡。当球员记录的更新取决于比赛中双方球员的行动时，任何严格的个人理性行动都可以在稳态均衡中得到支持。当记录更新只能依赖于玩家自己的操作时，可以支持的操作更少。在这里，我们关注囚徒困境，并将注意力限制在具有协调性的严格均衡上，这意味着匹配的合作伙伴永远不会在由他们的记录和预期持续收益引起的一次性博弈中达到帕累托主导的纳什均衡。如果舞台博弈是“严格超模和温和”或“强超模”，这种均衡可以支持完全合作，否则根本不允许合作。“超级合作者”记录的存在，即玩家与任何对手合作，对于支持在舞台游戏“严重”时的任何合作至关重要。