Deck 21: Game Theory

Question 1

A two-person game encompasses two players.

Answer 1

True

Question 2

A point of equilibrium is a value that is simultaneously the minimum of a row and the maximum of a column.

Answer 2

True

Question 3

In a zero-sum game, one player's gains represent another's exact losses.

Answer 3

True

Question 4

In a ________ game each player adopts a single strategy as an optimal strategy.

Question 5

The value of the game is the defensive player's gain and the offensive player's loss in a zero-sum game.

Question 6

In a strategy it is assumed that the payoff table is known to all players.

Question 7

In a game situation, it is assumed that the payoff table is known to all players.

Question 8

The payoffs for a mixed strategy game assumes that the game is played many times.

Question 9

In a mixed strategy game, players switch decision in response to the other player.

Question 10

A ________ is a plan of action followed by a player.

Question 11

With the minimax criterion, each player seeks to minimize maximum possible losses.

Question 12

In a ________ game one player's gains represent another player's exact losses.

Question 13

In a pure strategy game, each player adopts a single strategy as an optimal strategy.

Question 14

The best strategy for each player is his or her optimal strategy.

Question 15

Game theory addresses decision situations with two or more decision makers in competition.

Question 16

The value of the game is the offensive player's gain and the defensive player's loss in a zero-sum game.

Question 17

Game theory addresses decision situations with two or fewer decision makers in competition.

Question 18

The payoffs for a mixed strategy game assumes that the game is played exactly one time.

Question 19

A point of equilibrium is a value that is simultaneously the maximum of a row and the minimum of a column.

Question 20

A strategy is a plan of action followed by a player.

Question 21

What decision should be made by the optimistic decision maker?

Question 22

What decision should be made under minimax regret?

Question 23

The ________ method uses probabilities to determine the best strategy for each player.

Question 24

In the expected ________ method, a plan of strategies is determined by each player so that expected gain of one equals the expected loss of the other.

Question 25

In game theory, each player seeks to minimize maximum possible losses with the ________ criterion.

Question 26

In a(n) ________ game, players switch decisions in response to the decision of the other player and eventually return to the initial decisions, resulting in a closed loop.

Question 27

A(n) ________ occurs when the optimal strategy for each player results in the same payoff.

Question 28

In a pure strategy game the optimal strategy for each player results in the same payoff, called an ________ point.

Question 29

The local operations manager for the IRS must decide whether to hire one, two, or three temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.
If he uses the maximin criterion, how many new workers will he hire?

Question 30

A pure strategy game can be solved according to the ________ criterion.

Question 31

What decision should be made under minimax regret?

Question 32

A ________ game occurs when each player selects an optimal strategy that does not result in an equilibrium point when the minimax criterion is used.

Question 33

$$\begin{array} { | c | c | c | c | } \hline & \text { s1 } & \text { s2 } & \text { s3 } \\\hline \mathrm { d } _ { 1 } & 10 & 8 & 6 \\\hline \mathrm { d } _ { 2 } & 14 & 15 & 2 \\\hline \mathrm { d } _ { 3 } & 7 & 8 & 9 \\\hline\end{array}$$
If the probabilities of s1, s2, and s3 are 0.2, 0.4, and 0.4, respectively, then what decision should be made under expected value?

Question 34

Given the following payoff table:
What is the value of the game?

Question 35

What decision should be made by the conservative decision maker?

Question 36

A strategy is ________ and can be eliminated if all its payoffs are worse than the corresponding payoffs for another strategy.

Question 37

The local operations manager for the IRS must decide whether to hire one, two, or three temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.
If he uses the minimax regret criterion, how many new workers will he hire?

Question 38

If the probabilities of d1, d2, and d3 are 0.2, 0.5, and 0.3, respectively, then what decision should be made under expected value?

Question 39

The ________ for a mixed strategy game assumes that the game is played many times.

Question 40

What decision should be made by the conservative decision maker?

Question 41

The ________ criterion results in the maximum of the minimum payoffs.

A) minimax
B) maximax
C) maximin
D) minimin

Question 42

A ________ is a plan of action followed by a player.

A) game situation
B) strategy
C) value of the game
D) best strategy
E) pure strategy

Question 43

In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game:
If the station plans on running the game every day for 10 days, how much will they pay out?

Question 44

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below. $\begin{array} { l l c c } \hline && { \text { Company B } } \\&& \mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\&& \text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}$

Determine the proportion of time that each company should employ each strategy.

Question 45

Mary Schultz is the incumbent Senator from Ohio and John Henderson is her opponent in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the election. The following payoff table shows the various percentage point gains/losses in the polls for the two candidates based on their selection of certain political strategies.
Determine the optimal strategy and the optimal payoff for both players.

Question 46

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below. $\begin{array} { l l c c } \hline && { \text { Company B } } \\&& \mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\&& \text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}$
Determine the value of the game.

Question 47

The local operations manager for the IRS must decide whether to hire one, two, or three temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.
If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire?

Question 48

The expected value and expected opportunity loss criteria result in

A) the same decision.
B) different decisions.
C) similar decisions.
D) all of the above

Question 49

With the ________ criterion each player seeks to minimize maximum possible losses.

A) minimax
B) maximax
C) minimin
D) maximin

Question 50

The maximin approach to decision making refers to

A) minimizing the maximum return.
B) maximizing the minimum return.
C) maximizing the maximum return.
D) minimizing the minimum return.

Question 51

Regret is the difference between the payoff from the

A) best decision and all other decision payoffs.
B) worst decision and all other decision payoffs.
C) best decision and the worst decision payoffs.
D) none of the above

Question 52

Construct the payoff matrix for the game, "rock, paper, scissors" for 2 players, A and B. Assume that "paper covers rock", "rock breaks scissors," and "scissors cut paper." If player A wins, assign +1. If player A loses, assign -1.

Question 53

Given the following payoff/loss table for a mixed strategy game between two players:
Identify dominated strategy(s), if it (they) exist(s).

Question 54

Game theory assumes that players behave

A) logically.
B) emotionally.
C) rationally.
D) A, B, and C
E) A and B

Question 55

In a zero sum game one player's gains represent another's exact

A) gains.
B) losses.
C) gains and losses.
D) gains or losses.

Question 56

Mary Schultz is the incumbent senator from Ohio and John Henderson is her opponent in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the election. The following payoff table shows the various percentage point gains/losses in the polls for the two candidates based on their selection of certain political strategies.
Use the expected gain and loss method and determine the probability that each strategy will be used by each player.

Question 57

A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a

A) decision tree.
B) payoff table.
C) feasible region.
D) payback matrix.

Question 58

The ________ is the offensive player's gain and the defensive player's loss in a zero-sum game.

A) game situation
B) value of the game
C) strategy
D) best strategy
E) pure strategy

Question 59

Mary Schultz is the incumbent senator from Ohio and John Henderson is her opponent in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the election. The following payoff table shows the various percentage point gains/losses in the polls for the two candidates based on their selection of certain political strategies.
Use the expected gain and loss method and determine the equilibrium point.

Question 60

Determining the worst payoff for each alternative and choosing the alternative with the best of the worst payoffs is called a ________ criterion.

A) maximin
B) minimin
C) maximax
D) minimax

Question 61

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below. $\begin{array} { l l c c } \hline && { \text { Company B } } \\& &\mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\& &\text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}$
Determine the proportion of time that Company B should employ each strategy.

A) B₁: 12.5%, B₂: 87.5%
B) B₁: 25%, B₂: 75%
C) B₁: 37.5%, B₂: 62.5%
D) B₁: 50%, B₂: 50%
E) B₁: 62.5%, B₂:37.5%

Question 62

A(n) ________ game occurs when each player selects an optimal strategy that does not result in an equilibrium point when the minimax criterion is used.

A) optimal strategy
B) pure strategy
C) mixed strategy
D) best strategy

Question 63

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below. $\begin{array} { l l c c } \hline && { \text { Company B } } \\&& \mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\&& \text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}$
Determine the proportion of time that Company A should employ each strategy.

A) A₁: 12.5%, A₂: 87.5%
B) A₁: 25%, A₂: 75%
C) A₁: 37.5%, A₂: 62.5%
D) A₁: 50%, A₂: 50%
E) A₁: 62.5%, A₂: 37.5%

Question 64

In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game: $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Treasure Hunter Finds: } \\\begin{array} { l r r c } & & \$ 50 & \$ 100 \\\hline \text { Caller Guesses } & \$ 50 & \$ 50 & \$ 0 \\& \$ 100 & \$ 0 & \$ 100\end{array}$$ If the station plans on running the game every day for 10 days, how much will they pay out?

A) $250
B) $333
C) $500
D) $750
E) $667