Question 1

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

Accepted Answer

Example 2, in the context of decision theory, typically illustrates how individuals struggle to process and evaluate the probabilities and outcomes of compound lotteries (lotteries where the prize itself is a lottery), highlighting the limitations in human cognitive capacity for dealing with complex probabilistic information.

Question 2

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

Accepted Answer

Risk aversion in expected utility theory is represented by a concave utility function, as it reflects a diminishing marginal utility of wealth, meaning that the utility gained from an incremental unit of wealth decreases as wealth increases.

Question 3

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

Accepted Answer

It is based on the notion that people classify gains and losses differently.

Question 4

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

Accepted Answer

Gains and losses are classified in terms of a reference point. Reference points can change depending on the scenario or how the gamble is framed.

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.

Accepted Answer

Prospect Theory, developed by Daniel Kahneman and Amos Tversky, posits that people value gains and losses differently, leading to a value function that is generally concave for gains (implying risk aversion), convex for losses (implying risk seeking in the domain of losses), and steeper for losses than for gains, indicating that losses loom larger than gains.

Question 6

Khaneman and Tversky proposed a unique method for editing.

Accepted Answer

As the text explains, a decision-maker can arrive at very different choices depending on which order he employs each of the six editing criteria.

Question 7

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

Accepted Answer

Cumulative Prospect Theory extends Prospect Theory by incorporating rank-dependent probability weighting functions, which account for how people actually perceive probabilities, not as linear but in a distorted manner, making it a more accurate model of decision-making under risk.

Question 8

Rank dependent probability weights are sub-additive.

Accepted Answer

Rank dependent probability weights were introduced to deal with the suband super-additivity of probability weighting functions. By definition, they sum to 1 .

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.

Accepted Answer

Prospect theory suggests that individuals are more risk-averse when they perceive themselves to be in a domain of gains but become more risk-seeking in a domain of losses. Therefore, after losing money early (entering the loss domain), bettors are more likely to take risks on long-shots 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.

Accepted Answer

This is the prediction of expected utility theory. The "kink" at the reference point under prospect theory means that the utility function cannot be approximated by a straight line.

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.

Accepted Answer

The answer of What is the reflection effect?
A) The observation...

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.

Accepted Answer

Risk aversion is indicated by a concave utility function, which means that the second derivative of the utility function with respect to wealth is negative ($u''(x) < 0$). This leads to the condition $E[u(x)] < u(E[x])$, where the expected utility of a gamble is less than the utility of the expected value of the gamble, reflecting a preference for certainty over risk.

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) $\quad(x \mid 0)=\left\{\begin{array}{c}\ln (x), x>0 \ -\left(x^{2}\right), \quad x \leq 0\end{array}\right.$

Accepted Answer

Prospect Theory suggests that people value gains and losses differently, showing diminishing sensitivity for both, but with losses being felt more intensely than gains. Choice A reflects this by using a logarithmic function for gains ($x > 0$), indicating diminishing sensitivity, and a linear function for losses ($x < 0$), which can represent the stronger impact of losses, aligning with Prospect Theory's principles.

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) $u(x)=\frac{x^{4}}{.4}$

Accepted Answer

To determine the steepest slope at $x=2$, we calculate the first derivative of each utility function with respect to $x$ and evaluate it at $x=2$. The function with the highest derivative value at $x=2$ has the steepest slope.A) $u'(x)=\frac{1}{x}$, so at $x=2$, $u'(2)=\frac{1}{2}$.B) $u'(x)=\frac{1}{2\sqrt{x}}$, so at $x=2$, $u'(2)=\frac{1}{2\sqrt{2}}$.C) $u'(x)=.05$, so at $x=2$, $u'(2)=.05$.D) $u'(x)=\frac{4x^{3}}{.4}$, so at $x=2$, $u'(2)=\frac{4(2)^{3}}{.4}=80$.Option D has the highest derivative value at $x=2$, indicating the steepest slope.

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.

Accepted Answer

Prospect theory, developed by Daniel Kahneman and Amos Tversky, includes three main components: editing, probability weighting, and the value function. "Coding" is not one of the components; instead, the correct term related to how outcomes are perceived relative to a reference point is "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.

Accepted Answer

Coding involves the process where outcomes are classified as gains or losses, which is a crucial step in decision-making processes according to prospect theory.

Question 17

The reduction of a compound lottery occurs during which of the six editing tasks?
A) Simplification.
B) Segregation.
C) Cancellation.
D) Reduction.

Accepted Answer

The answer of The reduction of a compound lottery occurs...

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.

Accepted Answer

Prospect theory primarily deals with decisions under risk and uncertainty, often focusing on dichotomous choices. Non-dichotomous decisions, which involve more than two options, can complicate the application of prospect theory as it is traditionally framed.

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.

Accepted Answer

The isolation effect refers to the tendency of people to disregard components that are shared among choices, which is particularly relevant in compound lotteries where individuals may isolate and evaluate only the final outcomes rather than the entire structure of the lottery.

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) $\gamma, \delta$

Accepted Answer

The parameters $\alpha$ and $\beta$ typically concern the curvature of the value functions, indicating how the value or utility changes as the quantity of the good or outcome changes. This curvature reflects the concept of diminishing marginal utility.

Quiz 10: Prospect Theory and Decision Under Risk or Uncertainty

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

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

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

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

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.

Khaneman and Tversky proposed a unique method for editing.

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

Rank dependent probability weights are sub-additive.

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.

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

What is the reflection effect?

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

Let ug(x) u_{g}(x) ug​(x) be Julie's utility function over gains and ul(x) u_{l}(x) ul​(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?

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

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

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

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

Which of the following presents problem for prospect theory?

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

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

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?

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