Aumann discusses the impact of subjective probabilities and correlation on game theory. He shows that when mixed strategies are based on subjective random devices, two-person zero-sum games lose their strictly competitive nature, allowing cooperation and new equilibrium points with higher payoffs. In n-person games, new equilibrium points emerge that strictly dominate existing ones. Correlated strategies can achieve payoffs outside the convex hull of Nash equilibrium payoffs, even in two-person games. Aumann presents several examples illustrating these phenomena, showing how correlation can lead to better outcomes for all players. He also develops a formal model of randomized strategies, allowing for subjectivity and correlation. The paper concludes that while two-person games are not affected by subjective strategies, correlation can significantly improve payoffs in multi-player games. Aumann also discusses the concept of a posteriori equilibria, where players do not want to unilaterally change strategies after receiving information about the game state. The paper highlights the importance of subjective probabilities and correlation in game theory, showing how they can lead to more efficient outcomes.Aumann discusses the impact of subjective probabilities and correlation on game theory. He shows that when mixed strategies are based on subjective random devices, two-person zero-sum games lose their strictly competitive nature, allowing cooperation and new equilibrium points with higher payoffs. In n-person games, new equilibrium points emerge that strictly dominate existing ones. Correlated strategies can achieve payoffs outside the convex hull of Nash equilibrium payoffs, even in two-person games. Aumann presents several examples illustrating these phenomena, showing how correlation can lead to better outcomes for all players. He also develops a formal model of randomized strategies, allowing for subjectivity and correlation. The paper concludes that while two-person games are not affected by subjective strategies, correlation can significantly improve payoffs in multi-player games. Aumann also discusses the concept of a posteriori equilibria, where players do not want to unilaterally change strategies after receiving information about the game state. The paper highlights the importance of subjective probabilities and correlation in game theory, showing how they can lead to more efficient outcomes.