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Lecture_March9_MATH4321_12S

# Lecture_March9_MATH4321_12S - Swastika Method to find all...

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Unformatted text preview: Swastika Method to find all SE’s for 2x2 games: For 2x2 games, the players’ sets of strategies are parameterized by the unit interval. We can make use of this to devise a graphical method to find strategies that are best response to each other. • For each mixed strategy (q, 1-q) of Player II, we use the method as in 0-zero sum games to find the best response rows • Plot this in the unit square as a graph parameterized by q, 0  q  1 • For each mixed strategy (p, 1-p) of Player I, we use the method as in 0-zero sum games to find the best response columns • Plot this in the unit square in the above as a graph parameterized by p, 0  p  1 • The SE’s are the intersections of the two graphs Swastika Method to find SE for 2x2 games Swastika Method to find SE for 2x2 games Example: Find all SE’s for the following bimatrix game. • For each mixed strategy (p, 1-p) of Player I, we use the method as in 0-zero sum games to find the best response columns on B. • Plot this in the unit square in the above as a graph parameterized by p, 0  p  1 3, 2 2,1 3 2 2 1 , , 0,3 4, 4 4 3 4 A B   2 1 1 3 4 p p  3, 2...
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Lecture_March9_MATH4321_12S - Swastika Method to find all...

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