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We study whether the basic tenets of the theory of zero-sum games are still valid when players are uncertainty averse. We focus on games with one-sided information, in which the uninformed player is uncertain about the state of nature. Uncertainty aversion turns the underlying zero-sum game into a many-player, non-zero-sum game. We show that the uninformed player has a unique equilibrium payoff. We provide conditions under which there is a unique equilibrium payoff vector.