Lecture 1

Question 1

State the first axiom of preference relations.

Answer 1

A preference relation is complete if for any x,y, either x > y, y > x or x ~ y.

Question 2

State the second axiom of preference relations.

Answer 2

A preference relation is transitive if for any x,, y, z, if x >= y and y >= z, then x >= z.

Question 3

State the relationship between utility functions and axioms 1 and 2 of preference relations.

Answer 3

A preference relation satisfies A1 and A2 iff there exists some utility function that represents that preference relation.

Question 4

What function can be used to prove that if a preference relation satisfies A1 and A2, there exists a function that represents that relation?

Answer 4

The function linking an object to the number of objects it is prefered to.

Question 5

What is a simple Lottery?

Answer 5

A simple Lottery is a probability distribution over a set of prizes.

Question 6

What is a compound Lottery?

Answer 6

A compound lottery is a probability distribution over simple lotteries.

Question 7

What are the 4 axioms on preferences of lotteries?

Answer 7

1. Complete
2. Transitive
3. Continuity
4. Independence

Question 8

Give the definition of a Von Neumann Morgenstern Expected Utility Function.

Answer 8

Question 9

Prove the following proposition:

Answer 9

Question 10

Prove the following proposition:

Answer 10

See Slides 31-32 Lecture 1

Question 11

What is the expected Utility Theorem?

Answer 11

A preference relation satisfies A0 - A2 if and only if it has a von Neumann Morgenstern expected utility representation.

Question 12

Prove the if part of theorem 1.

Answer 12

Question 13

Give a proof of the expected Utility Theorem

Answer 13

Look at the Slides Mate

Question 14

Give a proof of Lemma 1