3. Choice under uncertainty

What is uncertainty?

opposite of certainty

• consequences depend on a probability, rather than happening for sure

• before knowing the realisation of a random variable

• with uncertainty there is risk(known probabilities) and ambiguity(unknown probabilities)

What is prospect?

list of consequences with associated probabilities

• p = (p₁: x₁;….; p_s : x_s)

What are consequences?

• finite set of consequences C = {x₁, x₂, …., x_s}

• S is the number of something in the world

What is probabilities?

What does p>q mean?

prospect p strictly preferred to prospect q

What is p ≥ q mean? funky version of signs

p is weakly preferred to q

What does p ~ q mean

indifference between p and q

• indifference does not mean that you don’t have a preference

• p ~ q means that both p ≥ q and q ≥ p - funky version

How do we find out the expected value

What is the St Petersburg paradox?

A game where you flip a coin repeatedly until you get heads

you will earn £2ⁿ, where n is the flip number at which I got heads

What does EV assume?

people base their decisions only on how much money they could receive but

• receiving £100 does not feel the same if you earn £1,000 per month than if you earn £10,000 oer month

• Choices may depend on factors other than economic profit

• solution transkate £ into utilities

What is the expected utility of prospect p (EU)?

What are the 3 attitudes towards risk?

• risk averse - hating

• risk seeking - loving

• risk neutral

What does attitude towards risk depend on

how the utility of the exoected value of the lottery compares to the expected utility of the lottery

What is certainty Equivalent (CE)?

amount which if recieved with certainty, gives the same utility as the EU of the lottery

What does a utility curve look like for a risk seeking agent?

What does the utility function look like for a risk averse agent?

What is Risk premium (RP)

difference between the expected value and the certainty equivalent