Finding an Equilibrium Point – 2x2 Zero Sum Game
{"Image DocumentName": "Finding an Equilibrium Point \u2013 2x2 Zero Sum Game", "Image ImageDescription": "Let\u2019s find the equilibrium point for the following 2x2 zero sum game: When a pitcher and batter face each other in a baseball game, we can consider each pitch as a simultaneous move zero-sum game. To make this an easier introductory example, let\u2019s suppose the pitcher only has two strategies: throw a curve or a fastball. And, assuming the batter commits to swing, let\u2019s assume the batter only has two strategies: swing expecting a fastball or swing expecting a curve ball. One final assumption that is not entirely unrealistic: This is a simultaneous move game because even though the pitcher commits to his strategy before the batter, we\u2019ll assume the batter does not have time to change strategies once the pitcher commits. The outcomes we associate with each pair of strategies is not whether the ball is hit or not but rather the probability the batter has of hitting the ball. Of course, the pitcher wants to minimize this probability and the batter wants to increase it.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}