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EMPHASIZING SADDLE POINTS THROUGH GAME THEORY: A CLASSROOM ACTIVITY

ABSTRACT In optimization problems, often students find a single extremum of a function that is assumed to be a maximum or a minimum. At best, saddle points are discarded when checking second order conditions en route to maxima or minima. Game theory provides a setting where saddle points are the solution concept. We introduce the necessary game-theoretic background and explain how game-theoretic experiments of the Matching Pennies game can be used as a classroom activity to develop intuition about saddle points. Paralleling how students learn to find extrema, we first consider finding saddle points on the interior of a set and then consider saddle-like points that appear on the boundary of compact sets. We conclude with a couple of examples from the game theory literature.