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Consider a family of zero-sum games indexed by parameter that determines each player's payoff functions and feasible strategies. The first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium values and strategies depend continuously and upper hemicontinously (respectively) on the parameter. This characterization uses two topologies in order to overcome a topological tension that arises when player's strategy sets are infinite-dimensional. The second main result is an application to Bayesian zero-sum games in which each player's information is viewed as a parameter.
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