3- Choice under Incomplete Information

Question 1

What is the difference between choice under uncertainty and risk?

Answer 1

Choice under risk is when the probabilities of the outcomes are meaningful and known

Question 2

What 2 elements summarise the decision set under uncertainty?

Answer 2

-Action space (A); all possible choices for agent
-States of the world (S); all possible environments

Question 3

How do you construct a payoff table?

Answer 3

Matrix of all the states of the world on top row and action space on left column

Question 4

What is the maximin criterion?

Answer 4

The best choice is the one with the greatest minimum utility payoff

Question 5

How do you construct a utility table?

Answer 5

Same as payoff table but each cell is the product of the utility of the action and state of world

Question 6

What is the maximax criterion?

Answer 6

The best choice is the one with the greatest maximum utility payoff

Question 7

What is the minimax-risk criterion?

Answer 7

The best choice is the one with the lowest maximum regret aka Regret Aversion

Question 8

What is the definition of regret?

Answer 8

Utility of (preferable) alternative action given a specific state

Question 9

What are 2 main critiques of the maximin criterion?

Answer 9

-Does not take into account payoffs/utilities that are not the worst
-Focuses exclusively on worst outcome (even if probability would be small)

Question 10

What is the definition of expected value?

Answer 10

The sum of probability-weighted outcomes

Question 11

How can you determine whether insurance is a good deal?

Answer 11

Establish a lifetime for product usage, calculate money spent on insurance in that period, establish breakeven probability of downside scenario

Question 12

What is the shape of a risk averse utility function?

Answer 12

Concave

Question 13

What is the shape of a risk prone/affine utility function?

Answer 13

Convex

Question 14

What is the shape of a risk neutral utility function?

Answer 14

Linear

Question 15

What is the Certainty Equivalent?

Answer 15

The amount of money such that an individual is indifferent between taking the lottery and taking the
money

Question 16

What is the Certainty Equivalent equation?

Answer 16

L is the number CE that satisfies the equation u(CE) = EU(L) i.e. expected lottery utility equals certain utility

Question 17

What are the 3 properties of the value function in prospect theory?

Answer 17

-Ranges over changes in endowment (not about total endowments)
-Steeper for losses than for gains
-Convex for losses and concave for gains

Question 18

How can you prove loss aversion from 2 value functions one for gains one for losses?

Answer 18

Get the first derivative for each domain, show the absolute value of the loss domain gradient is greater

Question 19

How can you prove risk-aversion/affinity for the value function of either the loss or gain domain?

Answer 19

Take the second derivative of the value function and show whether it’s convex or concave

Question 20

How do you calculate expected value of an upside and downside scenario for a prospect theory value function?

Answer 20

Sub in each scenario to respective value function, and multiply the probabilities on the outside

Question 21

What are the 2 ways individuals can bundle gains/losses?

Answer 21

-Integrate; evaluating net value of gains/losses
-Segregate; evaluating each gain/loss separately

Question 22

Why does Bundling violate rational choice theory?

Answer 22

Because utility functions are defined over total endowments/final outcomes

Question 23

How do you integrate gains/losses mathematically using value functions?

Answer 23

Sum the gains and losses for a single value of x and substitute into value function

Question 24

How do you segregate gains/losses mathematically using value functions?

Answer 24

Put each outcome into its own value function and sum them

Question 25

What is the silver lining effect?

Answer 25

Individuals are more satisfied if gains are segregated (due to risk-aversion in the gain frame)

Question 26

What is the cancellation effect?

Answer 26

Individuals are less dissatisfied if losses are integrated (due to risk-proneness in the loss frame)

Question 27

What is the Sure-Thing principle?

Answer 27

Rational decisions based on Expected Utility Theory should not be affected by sure things

Question 28

What does the Allais paradox show?

Answer 28

The sure-thing principle is systematically and predictably violated in real world decision making

Question 29

What is the Certainty Effect?

Answer 29

Decision-maker frequently overweight outcomes that are certain

Question 30

Define Ambiguity Aversion

Answer 30

If lotteries involve both, known (risky) and unknown (ambiguous) probabilities, subjects tend to avoid ambiguous outcomes

Question 31

What are the 3 main properties of the probability weighting function (π) in prospect theory?

Answer 31

-Perceived probability is increasing in underlying probability
-Yes and no certainties are understood as such
-Perception is greater/less as probability approaches 0/1