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In this work we consider online decision-making in settings where players want to guard against possible adversarial attacks or other catastrophic failures. To address this, we propose a solution concept in which players have an additional constraint that at each time step they must play a diversified mixed strategy: one that does not put too much weight on any one action. This constraint is motivated by applications such as finance, routing, and resource allocation, where one would like to limit one’s exposure to adversarial or catastrophic events while still performing well in typical cases. We explore properties of diversified strategies in both zero-sum and general-sum games, and provide algorithms for minimizing regret within the family of diversified strategies as well as methods for using taxes or fees to guide standard regret-minimizing players towards diversified strategies. We also analyze equilibria produced by diversified strategies in general-sum games. We show that surprisingly, requiring diversification can actually lead to higher-welfare equilibria, and give strong guarantees on both price of anarchy and the social welfare produced by regret-minimizing diversified agents. We additionally give algorithms for finding optimal diversified strategies in distributed settings where one must limit communication overhead.