Week 3 uncertainty Flashcards
expected value calculation
Probability of outcome x outcome +Probability of outcome x pay off outcome etc. (sum across)
expected utility theory
assess payoffs in terms of utility they give
expected utility calculation
probability of outcome * utility of payoff in that outcome
Axioms of expected utility theory
- Completeness- a preferred to b, b is preferred to a or a and b is indifferent
- Reflexivity- A is at least as good as itself
- Transitivity- if a is at least as good as b and b is at least as good as c then a must be at least as good as C
- independence of irrelevant alternatives. that the choice between two options should not be affected by the addition of a third, irrelevant option.
- Continuity
If there are three lotteries where a≥b≥c then there must exist some probability that a given lottery with the best thing you prefer and the worst outcome. There must be some value of p that will leave you indifferent between the probability of getting both the worst and best outcome and B.
What happens if 1-5 axioms hold
VNM utility function, and the agent will behave as if he is maximizing expected utility.
ordinal utillity
any utility function that preserves the preference ordering can represent the agents preferences
cardinal utlity
only a very specific transformation will represent the same preferences.
Only transformations which will be valid are… transformations with the original utility function and allowed to multiply by a positive constant and add another positive constant.
risk aversion
if they would choose a certain outcome over a fair gamble (one with the same expected value as the certain outcome).
U” is negative- second derivative is negative shows diminishing marginal utility.
degree of risk aversion
More concave vNM implies higher risk aversion
risk seeking
Prefers fair gamble over certain outcome, Second derivative of utility function is bigger than 0 meaning increasing marginal utility.
Risk neutral
Indifferent between fair gamble and certain outcome
Second derivative of utility function is equal to 0 therefore constant marginal utility.
certainty equivalent
the amount of certain payoff that would make the agent indifferent between the lottery and the certain payoff.
CE for Risk neutral
Certainty equilivant= expected value
CE for risk adverse
What level of certain payoff would leave this individual exactly indiffernt between certain payoff and lottery A.
CE<EV
Certainty equivalent for risk seeking
CE>EV i.e need to make risk more attractive
