Question: Problem # 1. Consider Rock-Paper-Scissors game. Assume there are three additional players, Superman, Kryptonite and Dynamite. Superman beats everything except Kryp- tonite, Dynamite beats Rock,

Problem # 1. Consider Rock-Paper-Scissors game. Assume there are three additional

Problem # 1. Consider Rock-Paper-Scissors game. Assume there are three additional players, Superman, Kryptonite and Dynamite. Superman beats everything except Kryp- tonite, Dynamite beats Rock, Krpytonite, and Paper, but gets beaten by Scissors. Kryp- tonite gets beaten by everything except Superman. Moreover, when Paper beats Rock, it is counted twice valuable compared to other encounters. a) (5pt) Find the payoff matrix. b) (5pt) Is there a pure strategy equilibrium? Find it if exists. If it doesn't exist, show that it doesn't exist. b) (10pt) Find the equilibrium achieving strategies and value of this game. Clearly demon- strate all your steps. Problem # 1. Consider Rock-Paper-Scissors game. Assume there are three additional players, Superman, Kryptonite and Dynamite. Superman beats everything except Kryp- tonite, Dynamite beats Rock, Krpytonite, and Paper, but gets beaten by Scissors. Kryp- tonite gets beaten by everything except Superman. Moreover, when Paper beats Rock, it is counted twice valuable compared to other encounters. a) (5pt) Find the payoff matrix. b) (5pt) Is there a pure strategy equilibrium? Find it if exists. If it doesn't exist, show that it doesn't exist. b) (10pt) Find the equilibrium achieving strategies and value of this game. Clearly demon- strate all your steps

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