Game theory has been extensively applied to elucidate the evolutionary mechanism of cooperative behaviour. Dilemmas in game theory are important elements that disturb the promotion of cooperation. An important question is how to escape from dilemmas. Recently, a dynamic utility function (DUF) that considers an individual's current status (wealth) and that can be applied to game theory was developed. The DUF is different from the famous five reciprocity mechanisms called Nowak's five rules. Under the DUF, cooperation is promoted by poor players in the chicken game, with no changes in the prisoner's dilemma and stag-hunt games. In this paper, by comparing the strengths of the two dilemmas, we show that the DUF is a novel reciprocity mechanism (sixth rule) that differs from Nowak's five rules. We also show the difference in dilemma relaxation between dynamic game theory and (traditional) static game theory when the DUF and one of the five rules are combined. Our results indicate that poor players unequivocally promote cooperation in any dynamic game. Unlike conventional rules that have to be brought into game settings, this sixth rule is universally (canonical form) applicable to any game because all repeated/evolutionary games are dynamic in principle.

博弈论已被广泛应用于阐明合作行为的进化机制。博弈论中的困境是干扰合作促进的重要因素。一个重要的问题是如何摆脱困境。最近，开发了一种动态效用函数（DUF），该函数考虑个人的当前状态（财富）并可以应用于博弈论。DUF与著名的五个互惠机制（称为Nowak的五个规则）不同。在DUF的领导下，可怜的玩家在鸡比赛中促进了合作，而囚徒的困境和搜寻雄鹿的比赛没有改变。在本文中，通过比较两个难题的优势，我们表明DUF是一种新颖的互惠机制（第六条规则），与Nowak的五个规则不同。我们还显示了当DUF和五个规则之一组合时，动态博弈论和（传统）静态博弈论在困境放松方面的差异。我们的结果表明，贫穷的玩家在任何动态游戏中都明确促进合作。与必须纳入游戏设置的常规规则不同，该第六条规则在所有游戏中都通用（规范形式），因为所有重复/进化游戏原则上都是动态的。