Lecture 3

Question 1

How do we maximise expected utility?

Answer 1

• Sum of the outcome of utility multiplied by the probability of the state
• Ai = what you can do
• Sj = possible ways the world can turn out
• Oij: Consequences of act, given a particular state
• e.g A: BBQ indoors/outdoors, S: Sunny vs Rain = 4 outcomes combining S & A
• Then have to assign a utility matrix to each of the combinations e.g bbq and sunny has a 100 utility = subjective numbers
• EU = Sum of (Utility x Probability of it occurring)

Question 2

What are the four axioms of expected utility theory?

Answer 2

• Cancellation: Sure-Thing principle
• Transitivity
• Dominance
• Invariance
• If a decision maker wants to maximise EU, they MUST obey these axioms otherwise it is not a good decision/EU

Question 3

What is the Sure thing principle?

Answer 3

• States of the world that give the same outcome regardless of someone’s choice can be eliminated from the choice problem
• Seen through the Allais Paradox as well as the Ellsberg Paradox
• As payout matrixes is the same as some of the outcomes are the same regardless of choice
• All axioms tend to be intuitive and applications of principles are complex