Multiple-Choice Exercises
For Game Theory
BSNS5230, J. Wang
1. In the game theory, the row player and the column player are assumed to have a same IQ.
a. True
b. False
2. In a _____________ problem, one of the two players is the Mother Nature.
a. game theory
b. decision theory
3. In a 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. 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.
6. A game is called "constant-sum" if
a. the payoffs of the two players are same in all circumstances.
b. the sum of gains of the two players remains unchanged in each circumstance.
c. the sum of gains of the two players is zero in every circumstance.
7. A "constant-sum" game can be converted into a "zero-sum" game.
a. True
b. False
8. There exists an equilibrium point in every payoff table in the game theory.
a. True
b. False
9. Which is correct in describing a "pure strategy"?
a. A pure strategy exists only when there is an equilibrium point in the game.
b. A pure strategy refers to the row player's strategy and the column player's strategy which
correspond to the equilibrium point.
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.
e. All of the above.
10. 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 point in a game.
d. All of the above.
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11. 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.
12. 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.
13. Suppose the row player has two alternatives A and B. With the equilibrium mixed strategy, the
expected payoff for the row player to take A is same as that of taking B.
a. True
b. False
14. Suppose both players are using the equilibrium mixed strategy. In what case can the row player 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.
15. 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 payoff 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.
16. A mixed strategy {for row player: 100% taking alternative A, 0% taking alternative B}, {for column
player: 0% taking alternative X, 0% taking alternative Y, 100% taking alternative Z} is in fact a pure
strategy.
a. True
b. False
17. If X and Y are two of the column player's strategy alternatives and X is dominated by Y in a game
theory problem, then the
a. loss with X is smaller than Y when the row player takes a certain strategy.
b. loss with X is larger than Y when the row player takes a certain strategy.
c. loss with X is always smaller than Y no matter what strategy the row player takes
d. loss with X is always larger than Y no matter what strategy the row player takes.
18. A dominated strategy can be removed from the decision table without affecting the result of decision.
a. True
b. False
Answers:
1.a 2.b 3.a 4.a 5.d 6.b 7.a 8.b 9.e 10.d 11.c 12.a 13.a 14.c 15.e 16.a 17.d 18.a
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