In repeated random matching games, cooperation can be maintained beyond the prisoner's dilemma using a new equilibrium concept called strongly uniform equilibrium. This concept ensures players make easy-to-follow strategies that lead to fair outcomes. The study also shows that in some cases, players can achieve payoffs that are better than what they could get individually. Additionally, the research establishes limits on the number of "free-riders" that can exist in society, particularly in the prisoner's dilemma game. Overall, the findings highlight how different equilibrium strategies can lead to sustainable cooperation in various game scenarios.