Decisions Under Uncertainity I

Decisions Under Uncertainity I - Prof. Dr. Reinhard H....

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1 Decision Theory SS 2009 3rd lecture, 28 Apr 2009 Decision under Uncertainty Prof. Dr. Reinhard H. Schmidt Copyright © Reinhard H. Schmidt
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2 Learning Objectives for Part II of the Course Students should understand the importance of describing a decision problems under uncertainty in a suitable way They should see why decision problems under uncertainty are different …. They should get to know, and to critizise, traditional decision criteria Based on this, they should understand the basic idea of the Bernoulli principle … and get a first view of the axioms underlying this approach
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3 Objectives and Contents of Part II • Traditional decision rules and their critique • The Bernoulli Criterion and its background • Risk attitudes, forms of utility functions, certainty equivalents and risk premiums • Deriving utility functions to express attitudes towards risk • Applications/applicability of Bernoulli principle
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4 Classification according to Frank H. Knight • Decisions under Certainty: Actions lead to unique consequences. • Decisions under Uncertainty (“Unsicherheit” or “unsichere Erwartungen”): Result are uncertain, they depend on uncontrollable factors such as environmental influences . • Knight’s famous – and seemingly plausible – classification: Risk: Probabilities for (relevant) states are known. True Uncertainty (“Ungewissheit”) : Probabilities for states are unknown.
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5 Uncertainty Decision matrix: How to compare a 1, a 2, a 3 ? One possibility: the dominance rule . z 1 z 2 z 3 a 1 7 3 5 a 2 2 8 9 a 3 1 2 4
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6 Dominance Rule Payments of a 1 and a 2 are higher in every state than those of a 3 . Hence a rational decision maker should never select a 3 . a 3 is dominated or not efficient. Problem: often no comparability between efficient alternatives (Note: This does not result in big indifference sets but alternatives are simply not comparable.) (Alternative formulation with probabilities: see next)
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7 Additional Decision Rules Maximin (Maximax)- rule (following A. Wald): Selevt the Alternative that maximises the objective value Φ (a i ) = minimum of line value (maximin) Ψ (a i ) = maximum of line value (maximax) Example: z 1 z 2 a 1 7 3 Φ (a 1 ) = 3 , Φ (a 2 ) = 2 , select a 1 ! a 2 2 8 Ψ (a 1 ) = 7 , Ψ (a 2 ) = 8 , select a 2 ! Why would anybody want to decide in that way?
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8 Additional Decision Rules Laplace Rule: Φ (a i ) = sum of line values Example: z 1 z 2 a 1 7 3 a 2 2 8 Φ (a1) = 10, Φ (a2) = 10 , indifferent! One possible interpretation of the Laplace rule: a decision maker assigns equal probabilities to all states.
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9 Additional Decision Rules Hurvicz-Rule: Φ (a i ) = a * best possible value + (1-a) * worst value with a as the „optimism-pessimism-index“ Example: z 1 z 2 z 3 a 1 7 5 4 a 2 2 7 8 If a = 1/3 Φ (a 1 ) = 5, Φ (a 2 ) = 4 , select a 1 !
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This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Schmidt during the Spring '09 term at Uni Frankfurt.

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Decisions Under Uncertainity I - Prof. Dr. Reinhard H....

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