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Behavioral eco-lect 4: Choice under risk and uncertainty part 4 (Minimax…
Behavioral eco-lect 4: Choice under risk and uncertainty part 4
Choice under uncertainty (a few simple models)
Maximin
: choose the alternative with the greatest minimum utility payoff
Example: “wet, miserable” is the worst possible outcome. So you bring an umbrella.
Maximax :
choose the alternative with the greatest maximum utility payoff
Example: “dry happy” is the best possible outcome. So you do not bring an umbrella.
Minimax-regret/ Minimax-risk
Regret payoffs
Minimax-regret
: choose the alternative with the lowest maximum regret.
Utility payoffs
zie tabel slide 40/55
for each state of the world compute the difference between “the maximum utility you could have obtained in this state” and “the utility you get under the alternative you consider” – this is your regret.
Example: bring the umbrella (2<3)
Maximin, maximax, and minimax-regret
Common in these criteria: you look only at the worst or best case scenario, irrespective of how likely you believe the various states of the world to be.
Umbrella-example: with maximin you bring an umbrella no matter whether you are in the UK or in California.
Are maximin, maximax, and minimax-regret rational/normative criteria?
More rational alternative to these criteria: assign subjective probabilities to all states of the world and then use expected utility to make your decision.
Choice under uncertainty (violations of expected utility)
Ellsberg
The ellsberg problem explained
In bets
I
and
IV
the exact probability of each outcome is clear.
In bets
II
and
III
the probabilities of the outcomes are
ambiguous.
People are
ambiguity averse.
Experiment 43-44/55
Diminishing sensitivity and Mental accounting
: Implications of diminishing sensitivity for decision making in general
Diminishing sensitivity to gains
Winning $75 in one go:
(1) reference point is 0
(2) gain of €75
Utility: 0 → U(75)
Winning €50 and €25 separately
:
(1) reference point is 0
(2) gain of €50
(3) reference point is 0 again
(4) gain of €25
Utility: 0 → U(50) → U(50) + U(25)
Diminishing sensitivity to gains
(with concave utility for gains) slide 49/55
Integrating or segregating outcomes
slide 47/55
If you have a prospect theory utility function with diminishing sensitivity to gains and losses, then it matters whether you integrate or segregate gains and losses.
Diminishing sensitivity to losses
(with convex utility for losses you prefer to integrate losses) slide 50/55