1. In the game theory, the row player and the column player are assumed to be humans who are equally smart. a. True b. False 2. In a a. game theory problem, one of the two players is the Super Nature. b. decision theory 3. In a zero-sum game theory problem, two players' interests are a. conflicting b. consistent 4. In a game theory problem, both players are supposed to have the same information as contained in the payoff/penalty table. a. True b. False 5. In the game table for the zero-sum game, the numbers represent a. the payoffs of the row player b. the losses of the column player c. Both a and b. 6. The value of a game is the row player's payoff and the column player's loss associated with the best strategy. a. True b. False 7. For the column player, the value of the game is a. the larger the better b. the smaller the better 8. A game is called "zero-sum" if a. the gains of the two players are summed to a constant in all circumstances b. one player's gain is exactly the other player's loss in every circumstance c. the sum of gains of the two players is zero in every circumstance d. Both b and c. 9. In a zero-sum game, the equilibrium strategy is the best strategy. a. True b. False 10. Given a mixed strategy (not necessarily equilibrium) for a zero-sum game, if the expected payoff of the row player is 74 , then the expected loss of the column player is a. 74 b. -74 c. Neither a nor b. We do not know, We need to calculate. 11. There exists a pure strategy in every problem in in the game theory. a. True b. False 12. In a zero-sum game, if max (row minimums) =min (column maximums\}, then a pure strategy exists. a. True b. False 13. Which best interprets the meaning of min (column maximum\}? a. Worst of the best outcomes of the column player. b. Worst of the worst outcomes of the column player. c. Best of the best outcomes of the column player. d. Best of the worst outcomes of the column player. 14. Which is correct in describing a "pure strategy"? a. A pure strategy exists only when there is an equilibrium value in the game. b. A pure strategy refers to an equilibrium strategy which contains one strategy for the row player and one strategy for the column player. c. The pure strategy is the best strategy for both row and column players. d. No player can be better off by unilaterally leaving the pure strategy. c. All of the above. 15. Strategy (row player (0.35,0.65), column player (0.7,0,0.3) \} is a. a pure strategy b. a mixed strategy 16. Which is correct in describing a "mixed strategy"? a. A mixed strategy is a set of probabilities for each player. b. A player randomly picks up a strategy alternative at a time according to the probabilities given in the mixed strategy. c. A mixed strategy is applied when there is no equilibrium value in a game. d. All of the above. 17. Suppose the row player has three alternatives, A, B, and C, for his strategy, and the mixed strategy for him is (0.4,0,0.6). Based on this mixed strategy, which strategy he should take? a. Strategy A. d. Strategy A and C, but not B. c. Strategy C. e. Randomiy pick one from the three altematives with probabilities 0.4,0, and 0.6 respectively. 18. A mixed strategy is a. equal to the value of the game b. given as a set of probabilities for each player c. telling that the alternative strategies must be combined d. calculated as the expected value of a player 19. How many value(s) of the game in a problem of game theory? a. One. b. Two, one for the row player, another for the column player. 20. Which is correct in describing an "equilibrium mixed strategy"? a. It is the best mixed strategy for either of the players. b. No player can benefit from unilaterally leaving it. c. Both a and b. 21. To find out the equilibrium mixed strategy, we use computer software QM a. True b. False 22. Which state is known as "equilibrium" in general? a. It is not stable. b. It is balanced, but if it is somehow off balance, it cannot come back to balance by itself. c. It is balanced, and if it is somehow off balance, it can come back to balance by itself. 23. Given any mixed strategy in a zero-sum game, a. it is always true that expected gain of row player = expected loss of column player. b. it is always true that expected gain of row player expected loss of column player c. it is always true that expected gain of row player $ expected loss of column player. d. None of above. 24. What is the consequence for a player to unilaterally leave the equilibrium strategy? a. He can be better off, if he is lucky. b. He can never be better off. c. If his change is noticed by the other player, he can be beat easily. d. Both b and c. 25. If a player stays with the equilibrium strategy, then he will not be hurt by whatever strategy the other player takes. a. True b. False 26. Suppose the row player has two alternatives A and B. With the equilibrium mixed strategy, the expected payoff of taking A is same as that of taking B. a. True b. False 27. Suppose both players are using the equilibrium mixed strategy. In what ease can the row player possibly be worse off? a. The column player changes his strategy while the row player remains unchanged. b. The row player changes his strategy while the column player remains unchanged. c. Both players change their strategies. 28. Suppose both players are using the equilibrium mixed strategy. What is correct in describing the consequences of row player's unilaterally leaving the strategy? a. The expected payoff of the row player does not change. b. The expected loss of the column player does not change. c. If the column player has noticed that the row player has left the equilibrium strategy, the column player can change his own strategy and beat the row player. d. Even the column player has noticed that the row player has left the equilibrium strategy, the column player can do nothing to take advantage of it and beat the row player. e. a,b and c. 29. Suppose both players are using the equilibrium mixed strategy. Which is correct in describing the consequences of both players leaving the equilibrium strategy? a. The value of the game will remain unchanged. b. The value of the game will change, and the two players can be both better off or both worse off. c. The value of the game will change, and one player will be better off, and the other is worse off. 30. A mixed strategy for row player: 100% taking alternative A,0% taking alternative B\}, \{for column player: 0% taking alternative X,0% taking altemative Y,100% taking alternative Z \} is in fact a pure strategy. a. True b. False (continued on the next page)