1 / 19

Choice under uncertainty – complete ignorance

Choice under uncertainty – complete ignorance. Problem. The set of possible actions/acts The set of states of nature For each action and state of nature a consequence For each consequence a payoff/utility A criterion according to which a decision maker evaluates alternative actions.

khanh
Download Presentation

Choice under uncertainty – complete ignorance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Choice underuncertainty – completeignorance

  2. Problem • The set of possible actions/acts • The set of states of nature • For each action and state of nature a consequence • For each consequence a payoff/utility • A criterion according to which a decision maker evaluates alternative actions

  3. Savage (1954) „Yourwifehasjustbroken 5 goodeggsinto a bowlwhenyoucome in and volunteer to finish the omelet. A sixthegg, which for somereasonmust be eitherused for the omeletorwastedaltogether, liesunbrokenbeside the bowl. Youmustdecidewhat to do with thisunbrokenegg…”

  4. Husband – agricultural scientist knows that in a randomly chosen sample of 6 eggs the probability of the sixth egg being bad conditional on first 5 eggs being good is 0.008. • Situation of risk • Husband – city guy, does not know anything about eggs; additionally the 5 eggs already broken into a bowl are white whereas the sixth egg has brownish dots on its shell and (according to the husband) seems to be of an extraordinary size • Situation of complete ignorance

  5. Exercise • Omelet with X eggs: 20*X • Cleaning Y bowls: • -10-10Y, if X>0 • 0, if X=0 • Throwing away a good egg: -20

  6. Exercise • Omelet with X eggs: 20*X • Cleaning Y bowls: • -10-10Y, if X>0 • 0, if X=0 • Throwing away a good egg: -20

  7. Choice function– intuition • Choice functionis a functionwhichassigns a decision to each set of feasibleoptions • Requirements: • Nonempty set of decisions • The set of decisionshas to be contained in the set of feasibleoptions • The choice functionshouldgeneratetransitivechoices • The choice functionshould be immune to manipulation (addinganirrelevantalternativeshould not change the choice) – Independence of IrrelevantAlternatives

  8. ??? A small trattoria,whichyoudon’tknow. Menu: • bistecca • pollo The cookarrives and announcesthat he canadditionallyprepare • trippa alla fiorentina

  9. Consistency and attractiveness of the choice rules 1) Maximin – itsdisadvantageispessimism 2) Hurwiczrule • How to chooseα? • Critique 1 A1 isoptimal, A2 also, but the combination of the twois not.

  10. 2) Hurwiczrule • Critique 2 • Both actionsoptimal • A1 seems to be much better • But we haveassumedcompleteignorance, so the aboveisequivalent to:

  11. 3) Minimaxregret (Savage) • Proposed to improveoverMaximin • Critique 1: Are the differences in utilities/payoffgoodmeasures of regret? • Critique 2: A small advantage in one stateexceeds the big one in anotherstate Payofftables: Regrettables:

  12. 3) Minimaxregret (Savage) • Proposed to improveoverMaximin • Critique 1: Are the differences in utilities/payoffgoodmeasures of regret? • Critique 2: A small advantage in one stateexceeds the big one in anotherstate Payofftables: Regrettables:

  13. 3) Minimaxregret (Savage) • Three kinds of rescuetransports • Aircraft • Short range • Longrange • Trucks • Headquarters: Wales • Three areas of earthquakerisk: • Wales • Iberianpeninsula • Azerbaijan

  14. 3) Minimaxregret (Savage) • Critique 3: The presence of anunwantedalternativemayhave influence on the chosenaction Payofftable: Regrettable: Payofftable: Regrettable:

  15. 3) Minimaxregret (Savage) • Critique 3: The presence of anunwantedalternativemayhave influence on the chosenaction Payofftable: Regrettable: Payofftable: Regrettable

  16. Solution to the problem?: Instead of comparingthemalltogether, comparethem in pairs Planebetterthanhelicopter Helicopterbetterthan trucks Trucks betterthanplane

  17. 4) Laplace rule (principle of insufficientreason) 5) The decisionmakercannotmakeuphismindwhichrule to use: Maximin, Hurwicz (α=0.75) or Laplace • He decides to choosethisactionwhichwins in pairwisecontest States of natureshould be chosencarefully Instransitive

More Related