3- Choice under Incomplete Information Flashcards
What is the difference between choice under uncertainty and risk?
Choice under risk is when the probabilities of the outcomes are meaningful and known
What 2 elements summarise the decision set under uncertainty?
-Action space (A); all possible choices for agent
-States of the world (S); all possible environments
How do you construct a payoff table?
Matrix of all the states of the world on top row and action space on left column
What is the maximin criterion?
The best choice is the one with the greatest minimum utility payoff
How do you construct a utility table?
Same as payoff table but each cell is the product of the utility of the action and state of world
What is the maximax criterion?
The best choice is the one with the greatest maximum utility payoff
What is the minimax-risk criterion?
The best choice is the one with the lowest maximum regret aka Regret Aversion
What is the definition of regret?
Utility of (preferable) alternative action given a specific state
What are 2 main critiques of the maximin criterion?
-Does not take into account payoffs/utilities that are not the worst
-Focuses exclusively on worst outcome (even if probability would be small)
What is the definition of expected value?
The sum of probability-weighted outcomes
How can you determine whether insurance is a good deal?
Establish a lifetime for product usage, calculate money spent on insurance in that period, establish breakeven probability of downside scenario
What is the shape of a risk averse utility function?
Concave
What is the shape of a risk prone/affine utility function?
Convex
What is the shape of a risk neutral utility function?
Linear
What is the Certainty Equivalent?
The amount of money such that an individual is indifferent between taking the lottery and taking the
money
What is the Certainty Equivalent equation?
L is the number CE that satisfies the equation u(CE) = EU(L) i.e. expected lottery utility equals certain utility
What are the 3 properties of the value function in prospect theory?
-Ranges over changes in endowment (not about total endowments)
-Steeper for losses than for gains
-Convex for losses and concave for gains
How can you prove loss aversion from 2 value functions one for gains one for losses?
Get the first derivative for each domain, show the absolute value of the loss domain gradient is greater
How can you prove risk-aversion/affinity for the value function of either the loss or gain domain?
Take the second derivative of the value function and show whether it’s convex or concave
How do you calculate expected value of an upside and downside scenario for a prospect theory value function?
Sub in each scenario to respective value function, and multiply the probabilities on the outside
What are the 2 ways individuals can bundle gains/losses?
-Integrate; evaluating net value of gains/losses
-Segregate; evaluating each gain/loss separately
Why does Bundling violate rational choice theory?
Because utility functions are defined over total endowments/final outcomes
How do you integrate gains/losses mathematically using value functions?
Sum the gains and losses for a single value of x and substitute into value function
How do you segregate gains/losses mathematically using value functions?
Put each outcome into its own value function and sum them
