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CHAPTER 10 4. Use the following normal-form game to answer the questions below. a. Identify the one-shot Nash equilibrium. The one-shot Nash equilibrium would be (A, C) If player 1 was to select A, the best strategy for player 2 would be C. If player 1 was to select B, player 2 would be better off choosing C. This makes C the dominant strategy for player 2. If player 2 chooses C, player 1 would be better off choosing A. If player 2 chooses D, player 1 would choose A. This makes A the dominant strategy for player 1 b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium? Explain. The answer is NO. This is because each player knows each other's strategy. They know that if one player cooperates, it's better that the other player doesn't cooperate. This would afford that player that doesn't cooperate a higher payoff. c. Suppose this game is innitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? Explain. 1 3mm X (1 + 0.06) =70+ 0.06 = 70 + 500 = 570 Yes, they can achieve payoffs that are better than the one-shot Nash equilibrium. The players will earn a payoff of $60 when they cooperate. If they don't cooperate, they will earn $'i'0 in the rst period and 30 thereafter. d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is B. If B is sufciently low, can players earn more than they could in the one-shot Nash equilibrium? Yes If the probability of the game ending after a given play is 0.42, the players would receive more than they could in the one-shot equilibrium. 60 >70+ 30 a ' a