Decision Problems

Question 1

3 components of a decision problem.

Answer 1

• ACTIONS
• OUTCOMES
• PREFERENCES

Question 2

Definition of PREFERENCE.

Answer 2

Is a binary relationship on the set of actions A.
Can be WEAK, STRICT, INDIFFERENT.

A preference is said to be:
- COMPLETE if there are not indecisiveness;
- TRANSITIVE if there are no cycles.

If a preference is either complete and transitive then it’s RATIONAL.

Question 3

Definition of UTILITY FUNCTION (also called payoff function).

Answer 3

Is an arbitrary quantification u(q) of the goodness coming from some input q.

Question 4

When is a player RATIONAL?

Answer 4

1. They act for their own good;
2. They are aware of all consequences of their acts.

UPDATED DEFINITON:
A player facing a decision problem with a payoff function u(.) over
outcomes is rational iff he chooses an action a∊A that maximizes his expected payoff.

Question 5

Definition of LOTTERY.

Answer 5

Is a set P of probability distributions p: X -> [0, 1] where X is a finite set X = {x1, …, xn} of outcomes.

Question 6

von Neumann–Morgenstern (VNM) utility theorem and axioms.

Answer 6

Under certain axioms of rational behavior, a decision-maker faced with risky (probabilistic) outcomes of different choices will behave as if he or she is maximizing the expected value of some function (see the expected utility theory).

Axioms:
1. Preference is complete and transitive;
2. Indipendence
3. Continuity

Question 7

3 types of RISK ATTIDUTE.

Answer 7

• Risk neutral: a player sees A and B as perfect substitute choices;
• Risk averse: a player prefers a degenerate lottery (the sure thing);
• Risk loving: reverse.

Question 8

Backward induction exercize.

Answer 8

1. Classify all nodes with P’s action into groups;
2. Compute expectations.