第十八章 Game Theory：Introduce the concept of game theory.18.1Game Theory:Game Theory[判断题] Monopoly always has constant elasticity demand.
18.2Dominant Strategy andNash equilibrium:Dominant Strategy andNash equilibrium
18.3Mixed Strategies:Mixed Strategies
18.4Sequential Games:Sequential Games
选项:[对, 错]
[单选题]A game has two players. Each player has two possible strategies. One strategy is called “cooperate”, the other is called “defect”. Each player writes on a piece of paper either a C for cooperate or a D for defect. If both players write C; they both get a payoff of $100. If both players defect they each get a payoff of 0. If one player cooperates and the other player defects, the cooperating player gets a payoff of S and the defecting player gets a payoff of T . To defect will be a dominant strategy for both players if:
选项:[ T > 2S, S < 0 and T > 100., S < T and T > 100., S + T > 100]
[单选题]In the town of Torrelodones, each of the N > 2 inhabitants has $100. They are told that they can all voluntarily contribute to a fund that will be evenly divided among all residents. If $F are contributed to the fund, the local K-Mart will match the private contributions so that the total amount to be divided is $2F. That is, each resident will get back a payment of $2F/N when the fund is divided. If people in town care only about their own net incomes, in Nash equilibrium, how much will each person contribute to the fund?选项:[$10, $20, 0, $50]
[单选题]Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the trough. If both pigs choose Wait, both get 2. If both pigs press the button then Big Pig gets 7 and Little Pig gets 3. If Little Pig presses the button and Big Pig waits at the trough, then Big Pig gets 10 and Little Pig gets 0. Finally, if Big Pig presses the button and Little Pig waits, then Big Pig gets 6 and Little Pig gets 1. In Nash equilibrium, 选项:[Little Pig will get a payoff of 3 and Big Pig will get a payoff of 7., The pigs must be using mixed strategies., Both pigs will wait at the trough. , Little Pig will get a payoff of 1 and Big Pig will get a payoff of 6.]
[单选题]A famous Big Ten football coach had only two strategies. Run the ball to the left side
of the line. Run the ball to the right side. The defense can concentrate forces on the left side or the right side. If the opponent concentrates on the wrong side, his offense is sure to gain at least 5 yards. If the defense defended the left side and the offense ran left, it gain only 1 yard. If the opponent defended the right side when the offense ran right, the offense would still gain at least 5 yards with probability 0.70. It is the last play of the game and the famous coach's team is on offense. If it makes 5 yards or more it wins, if not it loses. Both sides choose Nash equilibrium strategies. In equilibrium the offense:
选项:[is sure to run to the right side., will run to the right side with probability 0.77., will run to the right side with probability 0.87., will run to the two sides with equal probability.]
[判断题]A situation where everyone is playing a dominant strategy must be a Nash equilibrium.选项:[错, 对]
[判断题]In a Nash equilibrium, everyone must be playing a dominant strategy选项:[错, 对]
[判断题]In the prisoners' dilemma game, if each prisoner believed that the other prisoner would deny the crime, then both would deny the crime.选项:[错, 对]
[判断题]A general has the two possible pure strategies, sending all of his troops by land or all of his troops by sea. An example of a mixed strategy is where he sends 1=4 of his troops by land and 3=4 of his troops by sea.选项:[对, 错]
[判断题]In Nash equilibrium, each player is making an optimal choice for herself, given the choices of the other players选项:[错, 对]
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