Deck 10: Prospect Theory and Decision Under Risk or Uncertainty

Question 1

Example 2 suggests that individuals have limited cognitive capacity to deal with compound lotteries.

Answer 1

True

Question 2

Under expected utility theory, risk aversion implies a concave utility function and vice versa.

Answer 2

True

Question 3

Prospect theory is based on the notion that people classify gains and losses in the same way.

Answer 3

False

Question 4

A gain is always greater than 0 and a loss is always less than 0 .

Question 5

Prospect Theory suggests that the utility function is convex over losses and also that the slope of the utility function over losses is steeper than the slope of the utility function over gains.

Question 6

Khaneman and Tversky proposed a unique method for editing.

Question 7

When Prospect Theory uses rank dependent probability weighting functions it is known as Cumulative Prospect Theory.

Question 8

Rank dependent probability weights are sub-additive.

Question 9

In Example 3, Prospect theory can rationalize the behavior of betting on the favorites early in the night and the long-shots later in the night because bettors tend to lose money early in the night and then are operating in the loss domain later in the night.

Question 10

Prospect Theory predicts that risk aversion over small gambles implies that decisionmakers will avoid risk at almost any cost in large gambles.

Question 11

What is the reflection effect?

A) The observation that individuals are risk averse over gains and risk-loving over losses.
B) The observation that individuals are risk loving over gains and risk-averse over losses.
C) The observation that risk preferences switch between risk-loving and risk aversion depending on whether the outcome is a gain or loss.
D) The observation that risk aversion observed over small gambles implies unreasonable levels of risk aversion over large gambles.

Question 12

Under expected utility theory, which of the following implies risk aversion?

A) $E u(x)<u(E(x))$ .
B) $x_{c e}>E(x)$
C) $u^{\prime \prime}(x)>0$
D) The utility function is convex.

Question 13

Let $u_{g}(x)$ be Julie's utility function over gains and $u_{l}(x)$ her utility function over losses. If Julie's preferences are best described with Prospect Theory, which of the following is an example of Julie's value function?

A) $\quad v(x \mid 0)= \begin{cases}\ln (x), & x>0 \\ 0, & x=0 \\ -x, & x<0\end{cases}$
B) $\quad v(x \mid 0)= \begin{cases}\mathrm{X}, & x>0 \\ 0, & x=0 \\ -\ln (-x), & x<0\end{cases}$
C) $\quad v(x \mid 0)=\left\{\begin{array}{l}x, x>0 \\ x, x=0 \\ x, x<0\end{array}\right.$
D) $\quad(x \mid 0)=\left\{\begin{array}{c}\ln (x), x>0 \\ -\left(x^{2}\right), \quad x \leq 0\end{array}\right.$

Question 14

At $x=2$ which utility function has the steepest slope?

A) $u(x)=\ln (x)$
B) $u(x)=\sqrt{x}$
C) $u(x)=.05 \mathrm{x}$
D) $u(x)=\frac{x^{4}}{.4}$

Question 15

All of the following are one of the three components of prospect theory proposed by Khaneman and Tversky EXCEPT:

A) Editing
B) Coding.
C) Probability Weighting.
D) Value Function.

Question 16

Under which of the six editing tasks will an individual classify outcomes as gains or losses?

A) Classification.
B) Segregation.
C) Cancellation.
D) Coding.

Question 17

The reduction of a compound lottery occurs during which of the six editing tasks?

A) Simplification.
B) Segregation.
C) Cancellation.
D) Reduction.

Question 18

Which of the following presents problem for prospect theory?

A) Non-dichotomous decisions
B) The reflection effect.
C) Misperception of probabilities.
D) Reference points.

Question 19

The isolation effect concerns which of the following types of lotteries:

A) Lotteries with non-dichotomous outcomes.
B) Lotteries over small gambles.
C) Lotteries over large gambles.
D) Compound lotteries.

Question 20

In Example 2, which of the parameters concern the curvature of the value functions?

A) $\alpha, \gamma$
B) $\beta, \gamma$
C) $\alpha, \beta$
D) $\gamma, \delta$

Question 21

In Example 2, suppose $\lambda=1$ . Which of the following statements would be true?

A) The utility function is concave in losses.
B) The utility function is convex in gains.
C) The utility function does not display loss aversion.
D) The value function over losses is linear.

Question 22

Renee plans a night out at the casino. On the way to the casino, she is pulled over for speeding and gets a $\$ 100$ speeding ticket. She incorporates this into her nightly expenses. Thus, when Renee arrives at the casino, which gamble does prospect theory suggest she'll prefer.

A) Renee will be indifferent between all gambles.
B) $\$ 50$ for sure.
C) $\$ 100$ with probability .5.
D) $\$ 200$ with probability.25.

Question 23

William has a utility function given by $U(x)=\ln (\mathrm{x})$ . He faces a gamble that pays 10 with probability .5 and 15 with probability .5 . What is William's certainty equivalent - that is, what sure amount must he receive in order to be indifferent between the gamble and this sure amount?
a. Find $x_{C E}$ if William's utility was given by $U(x)=x$
b. Find $x_{C E}$ if William's utility was given by $U(x)=x^{2}$ .

Question 24

Consider the following compound lotteries: first a coin is flipped. If the coin comes up heads, you get to play out either simple lottery A or simple lottery B, where lottery A is given by
$54 \%$ chance of $\$ 99$ and lottery B is given by a $24 \%$ chance of $\$ 199$ . Before flipping the coin, you must choose between lottery A and lottery B.
a. Suppose you edit in the following order: Cancelation, Simplification. What do you perceive the final lottery choices to be?
b. Now suppose you edit in the following order: Combination, Simplification. What do you perceive the final lottery choices to be?

Question 25

Polly is betting at the racetrack. At the beginning of the evening she bets on the favorites and wins more money than she loses. During the end of the evening, Polly decides to bet on some long-shots. Can prospect theory rationalize her behavior?