In this chapter, we (a) present the definition and game theory interpretation of saddle points, (b) describe primal and dual optimization problems induced by an antagonistic game, (c) provide a characterization of saddle points in terms of optimal solutions and optimal values of primal and dual problems induced by the game, and (d) formulate and prove he Minimax Lemma and the Sion--Kakutani Theorem on existence of saddle points in convex--concave antagonistic games.
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