Exam 9: Decision Under Risk and Uncertainty

Consider four gambles: A,B, C, D. If $A>B$ and $C>D$ and my preferences satisfy the independence axiom, then what must be true for any $p \in[0,1]$ ?

Both the outcome effect and the certainty effect violate the independence axiom.

Figure 9.1 reflects the following idea: as $x$ increases above $y$ then the amount of utility I get from choosing $x$ over $y$ increases at an increasing rate; as $x$ decreases below $y$ then amount of utility I lose from choosing $x$ over $y$ decreases at a decreasing rate.

Regret aversion always allows for violations of transitivity.

Similarity is

Under $\alpha-\operatorname{maxmin}$ expected utility theory, the decision-maker is more ambiguous averse the more weight he puts on the highest probability of the preferred outcome occuring.

Consider three outcomes: $\mathrm{a}, \mathrm{b}, \mathrm{c}$ such that $a>b>c$ . Regret aversion implies which of the following?

All of the following theories seek to explain deviations from the rational model of behavior at extreme probabilities, except

The certainty effect is a rational preference for gambles with a certain outcome.

Regret theory differs from Expected Utility theory in which way?

Consider two gambles: Gamble A: $a=\$ 100$ with probability $p_{A}=.4$ and $\$ 0$ with probability .6. Gamble B: $b=\$ 75$ with probability $p_{B}=.45$ and $\$ 0$ with probability .55 . Use the similarity algorithm to indicate whether you would choose Gamble A or Gamble B.

Knightian risk refers to situations in which

Using the gambles in Example 3, use the common outcome effect to show how the following preferences: $A>B, D>C$ violates the independence axiom.

The Independence Axiom describes how people should value a single gamble with complex probabilities.

Maurice has a utility function such that $u(250)-u(125)<u(125)-u(0)$ and Lucy has a utility function such that $u(250)-u(125)=u(125)-u(0)$ . Who is more risk averse?

Suppose there are two jars. In Jar $1 \mathrm{I}$ know that there are 10 white balls and either 5 or 20 black balls. In Jar 2 I know that there are 10 red balls and either 10 or 30 black balls. I receive $\$ 5$ if a white ball is drawn from jar 1 and $\$ 10$ if a red ball is drawn from jar 2 and 0 otherwise. a. Suppose that I am risk-neutral. Using maxmin expected utility theory, do I draw from jar 1 or jar 2 and what is the value of my maxmin expected utility? b. Now suppose I am risk-averse, with a utility function given by $U(x)=\ln (x)$ . Do I choose Jar 1 or Jar 2 ?

With probability weighting, the weighting function $\pi(p)$ is convex below some threshold $\bar{p}$ and concave above some threshold $\bar{p}$ .

Consider gamble A: $\$ 80$ with probability .4 and $\$ 100$ with probability .6. Which of the gambles stochastically dominate gamble $\mathrm{A}$ .

Which of the following allows for the slope of indifference curve to depend on the level of utility?

Regret aversion is offered as an alternative to Expected Utility Theory in order to understand which of the following phenomena: