Deck 5: Utility Game Theory

Question 1

The expected monetary value approach and the expected utility approach to decision making usually result in the same decision choice unless extreme payoffs are involved.

Answer 1

True

Question 2

Given two decision makers,one risk neutral and the other a risk avoider,the risk avoider will always give a lower utility value for a given outcome.

Answer 2

False

Question 3

The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.

Answer 3

True

Question 4

The risk premium is never negative for a conservative decision maker.

Question 5

A risk avoider will have a concave utility function.

Question 6

The decision alternative with the best expected monetary value will always be the most desirable decision.

Question 7

A game has a pure strategy solution when both players' single-best strategies are the same.

Question 8

The logic of game theory assumes that each player has different information.

Question 9

When the payoffs become extreme,most decision makers are satisfied with the decision that provides the best expected monetary value.

Question 10

A game has a saddle point when pure strategies are optimal for both players.

Question 11

The expected utility is the utility of the expected monetary value.

Question 12

A risk neutral decision maker will have a linear utility function.

Question 13

Generally,the analyst must make pairwise comparisons of the decision strategies in an attempt to identify dominated strategies.

Question 14

When monetary value is not the sole measure of the true worth of the outcome to the decision maker,monetary value should be replaced by utility.

Question 15

The outcome with the highest payoff will also have the highest utility.

Question 16

Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.

Question 17

With a mixed strategy,the optimal solution for each player is to randomly select among two or more of the alternative strategies.

Question 18

The utility function for a risk avoider typically shows a diminishing marginal return for money.

Question 19

A game has a saddle point when the maximin payoff value equals the minimax payoff value.

Question 20

To assign utilities,consider the best and worst payoffs in the entire decision situation.

Question 21

If the payoff from outcome A is twice the payoff from outcome B,then the ratio of these utilities will be

A)2 to 1.
B)less than 2 to 1.
C)more than 2 to 1.
D)unknown without further information.

Question 22

When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery,the decision maker is

A)a risk avoider.
B)a risk taker.
C)an optimist.
D)an optimizer.

Question 23

The expected utility approach

A)does not require probabilities.
B)leads to the same decision as the expected value approach.
C)is most useful when excessively large or small payoffs are possible.
D)requires a decision tree.

Question 24

When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis),the function appears as

A)a straight line
B)a convex curve
C)a concave curve
D)an 'S' curve

Question 25

The purchase of insurance and lottery tickets shows that people make decisions based on

A)expected value.
B)sample information.
C)utility.
D)maximum likelihood.

Question 26

Which of the following statements about a dominated strategy is false?

A)A dominated strategy will never be selected by a player.
B)A dominated strategy exists if another strategy is at least as good regardless of what the opponent does.
C)A dominated strategy is superior to a mixed strategy.
D)A dominated strategy can be eliminated from the game.

Question 27

The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

A)the indifference probability.
B)the lottery probability.
C)the uncertain probability.
D)the utility probability.

Question 28

A 3 x 3 two-person zero-sum game that has no optimal pure strategy and no dominated strategies

A)can be solved using a linear programming model.
B)can be solved algebraically.
C)can be solved by identifying the minimax and maximin values.
D)cannot be solved.

Question 29

Utility reflects the decision maker's attitude toward

A)probability and profit
B)profit,loss,and risk
C)risk and regret
D)probability and regret

Question 30

For a two-person,zero-sum,mixed-strategy game,each player selects its strategy according to

A)what strategy the other player used last.
B)a fixed rotation of strategies.
C)a probability distribution.
D)the outcome of the previous game.

Question 31

If it is optimal for both players in a two-person,zero-sum game to select one strategy and stay with that strategy regardless of what the other player does,the game

A)has more than one equilibrium point.
B)will have alternating winners.
C)will have no winner.
D)has a pure strategy solution.

Question 32

Any 2 X 2 two-person,zero-sum,mixed-strategy game can be solved algebraically.

Question 33

When consequences are measured on a scale that reflects a decision maker's attitude toward profit,loss,and risk,payoffs are replaced by

A)utility values.
B)multicriteria measures.
C)sample information.
D)opportunity loss.

Question 34

A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(−25000)+ (1 − p)(5000).If the utility of −25,000 is 0 and of 5000 is 1,then the utility of −10,000 is

A).5
B).6
C).4
D)4

Question 35

Values of utility

A)must be between 0 and 1.
B)must be between 0 and 10.
C)must be nonnegative.
D)must increase as the payoff improves.

Question 36

For a game with an optimal pure strategy,which of the following statements is false?

A)The maximin equals the minimax.
B)The value of the game cannot be improved by either player changing strategies.
C)A saddle point exists.
D)Dominated strategies cannot exist.

Question 37

A dominated strategy will never be selected by the player.

Question 38

If the maximin and minimax values are not equal in a two-person zero-sum game,

A)a mixed strategy is optimal.
B)a pure strategy is optimal.
C)a dominated strategy is optimal.
D)one player should use a pure strategy and the other should use a mixed strategy.

Question 39

A decision maker whose utility function graphs as a straight line is

A)conservative.
B)risk neutral.
C)a risk taker.
D)a risk avoider.

Question 40

For a two-person zero-sum game,which one of the following is false?

A)The gain for one player is equal to the loss for the other player.
B)A payoff of 2 for one player has a corresponding payoff of −2 for the other player.
C)The sum of the payoffs in the payoff table is zero.
D)What one player wins,the other player loses.

Question 41

If a game larger than 2 X 2 requires a mixed strategy,we attempt to reduce the size of the game by

A)identifying saddle points
B)looking for dominated strategies
C)inverting the payoff matrix
D)eliminating negative payoffs

Question 42

A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs
For the lottery p(80)+ (1 − p)(−50),this decision maker has assessed the following indifference probabilities
Rank the decision alternatives on the basis of expected value and on the basis of expected utility.

Question 43

Explain how utility could be used in a decision where performance is not measured by monetary value.​

Question 44

Determine decision strategies based on expected value and on expected utility for this decision tree.Use the utility function

Question 45

Three decision makers have assessed utilities for the problem whose payoff table appears below.

a.Plot the utility function for each decision maker.
b.Characterize each decision maker's attitude toward risk.
c.Which decision will each person prefer?

Question 46

A decision maker has the following utility function
What is the risk premium for the payoff of 50?

Question 47

The Dollar Department Store chain has the opportunity of acquiring either 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores and its president estimates P(s₁)= .4,P(s₂)= .3,P(s₃)= .1,and P(s₄)= .2.The utility has also been estimated.Given the payoffs (in $1,000,000's)and utility values below,which decision should Dollar make?

Question 48

Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy.The fire statistics indicate that in a given year the probability of property damage in a fire is as follows:

a.If Burger Prince was risk neutral,how much would they be willing to pay for fire insurance?
b.If Burger Prince has the utility values given below,approximately how much would they be willing to pay for fire insurance?

Question 49

Game theory models extend beyond two-person,zero-sum games.Discuss two extensions (or variations).​

Question 50

Explain the relationship between expected utility,probability,payoff,and utility.​

Question 51

Draw the utility curves for three types of decision makers,label carefully,and explain the concepts of increasing and decreasing marginal returns for money.​

Question 52

Chez Paul is contemplating either opening another restaurant or expanding its existing location.The payoff table for these two decisions is:
Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and −$80,000 with probability (1−p)as follows:

a.Is Paul a risk avoider,a risk taker,or risk neutral?
b.Suppose Paul has defined the utility of −$80,000 to be 0 and the utility of $160,000 to be 80.What would be the utility values for −$40,000,$20,000,and $100,000 based on the indifference probabilities?
c.Suppose P(s₁)= .4,P(s₂)= .3,and P(s₃)= .3.Which decision should Paul make? Compare with the decision using the expected value approach.

Question 53

To select a strategy in a two-person,zero-sum game,Player A follows a ______ procedure and Player B follows a ______ procedure.

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

Question 54

When and why should a utility approach be followed?​

Question 55

Super Cola is considering the introduction of a new 8 oz.root beer.The probability that the root beer will be a success is believed to equal .6.The payoff table is as follows:
Company management has determined the following utility values:

a.Is the company a risk taker,risk averse,or risk neutral?
b.What is Super Cola's optimal decision?

Question 56

Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.​