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Ettore Damiano

Solutions to Chapter 4 ExercisesSOLVED EXERCISESS1False A dominant strategy yields you the highest payoff available to you against each of your opponents strategies Playing a dominant strategy does not guarantee that you end up with the highest of all possible payoffs In the prisoners dilemma game both players have dominant strategies but neither gets the highest possible payoff in the equilibrium of the gameS2aFor Row Up strictly dominates Down so Down may be eliminated For Column Right strictly dominates Left so Left may be eliminated These actions leave the purestrategy Nash equilibrium Up RightbRow has no dominant strategy but Right dominates Left for Column who prefers small numbers this being a zerosum game After eliminating Left for Column Up dominates Down for Row so Down is eliminated leaving the purestrategy Nash equilibrium Up Right cThere are no dominated strategies for Row For Column Left dominates Middle and Right Thus these two strategies may be eliminated leaving only Left With only Left remaining for Row Straight dominates both Up and Down so they are eliminated making the purestrategy Nash equilibrium LeftStraight dThe game is solved using iterated dominance Column has no dominated strategies For Row Up dominates Down so Down may be eliminated Then East dominates North so it is eliminated Then Up dominates Low so it is eliminated Then East dominates West so it is eliminated Then Up dominates High so it is eliminated leaving only Up With only Up remaining East dominates South giving the purestrategy Nash equilibrium Up EastS3aBy Minimax the minima for Rows strategies are 3 for Up and 1 for Down Row wants to receive the maximum of the minima so Row chooses Up The minima for Columns strategies are 2 for Left and 1 for Right Column wants to receive the maximum of the minima so Column chooses Right Again the purestrategy Nash equilibrium is Up RightSolutions to Chapter 4 Solved Exercises1 of 7
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