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Fundamentals of Decision Theory Models

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Deciding Between Job Offers Company A In a new industry that could boom or bust. Low starting salary, but could increase rapidly. Located near friends, family and favorite sports team. Company B Established firm with financial strength and commitment to employees. Higher starting salary but slower advancement opportunity. Distant location, offering few cultural or sporting activities. Which job would you take?

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Good Decisions vs. Good Outcomes A structured approach to decision making can help us make good decisions, but cant guarantee good outcomes. Good decisions sometimes result in bad outcomes.

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Introduction Decision theory is an analytical and systematic way to tackle problems A good decision is based on logic.

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The Six Steps in Decision Theory 1.Clearly define the problem at hand 2.List the possible alternatives 3.Identify the possible outcomes & criteria 4.List the payoff or profit of each combination of alternatives and outcomes 5.Select one of the mathematical decision theory models 6.Apply the model and make your decision

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Types of Decision-Making Environments Type 1: Decision-making under certainty decision-maker knows with certainty the consequences of every alternative or decision choice. (You know exact outcome; eg Savings Account) Type 2: Decision-making under risk decision-maker does know the probabilities of the various outcomes (You know the probability of each outcome; e.g. roll of die) Type 3: Decision-making under uncertainty decision-maker does not know the probabilities of the various outcomes (You know nothing, it is a wild guess at best)

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Decision-Making Under Risk n nature, of states ofnumber the to 1 j where )P(S*Payoff i) ativeEMV(Altern n 1j j S j Expected Monetary Value: ( Sum of the probabilities and outcome )

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Example You recently inherited $1,000 and are considering investing it in varied financial instruments. After Analyzing the economy (possibility of it being good or poor ) and the returns you can make in these conditions, you develop the following payoff table…

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Decision Table State Of Nature Decision AlternativeGood EconomyPoor Economy Portfolio 1 (high risk)80-20 Portfolio 2 (med risk)3020 Portfolio 3 (low risk)23 Probability Which portfolio should you invest in, that will maximize your returns?

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Decision Table State Of Nature Decision AlternativeGood EconomyPoor EconomyEMV Portfolio 1 (high risk) Portfolio 2 (med risk) Portfolio 3 (low risk)22 Probability What is the maximum amount that should be paid for perfect forecast of the economy?

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Expected Value of Perfect Information (EVPI) EVPI EVPI places an upper bound on what one would pay for additional information EVPI EVPI is the expected value with perfect information minus the maximum EMV EVPIEV|PIEMV EVPI = EV|PI - maximum EMV

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EVPI State Of Nature Decision AlternativeGood EconomyPoor EconomyEMV Portfolio 1 (high risk)80-20 Portfolio 2 (med risk) Portfolio 3 (low risk)22 Probability EMV EVPI = Expected Value with Perfect Information - max(EMV) = [ ] – 23 = $16.4

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Expected Opportunity Loss EOL EOL is the cost of not picking the best solution EOL EOL = Expected Regret Work it the same way as EMV but just use the regret instead of payoffs.

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EOL Table State Of Nature Decision AlternativeGood EconomyPoor EconomyEOL Portfolio 1 (high risk)80 – 80 = 022 – (-20) = 42 Portfolio 2 (med risk)80 – 30 = 5022 – 20 = 2 Portfolio 3 (low risk)80 – 22 = 5822 – 22 = 0 Probability0.30.7

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EOL Table State Of Nature Decision AlternativeGood EconomyPoor EconomyEOL Portfolio 1 (high risk) Portfolio 2 (med risk) Portfolio 3 (low risk) Probability0.30.7

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Sensitivity Analysis P1-P EMV(high risk) = $80P + (-$20) (1-P) P1-P EMV(med risk) = $30P + $20(1-P) P1-P EMV(low risk) = $22P + $22(1-P)

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Sensitivity Analysis - continued EMV (Med Risk) EMV(High Risk) EMV(low Risk)

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Decision Making Under Uncertainty Maximax Maximin Equally likely (Laplace) Criterion of Realism Minimax Regret

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Decision Making Under Uncertainty Maximax - Choose the alternative with the maximum output States of Nature Favorable Mkt ($) Unfavorable Mkt ($) Maximax Construct Large Plant 200, ,000200,000 Construct Small Plant 100,000-20,000100,000 Do Nothing000

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Decision Making Under Uncertainty Maximin - Choose the alternative with the maximum minimum output States of Nature Favorable Mkt ($) Unfavorable Mkt ($) Maximin Construct Large Plant 200, ,000-18,000 Construct Small Plant 100,000-20,000 Do Nothing000

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Decision Making Under Uncertainty Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV States of Nature Favorable Mkt ($) Unfavorable Mkt ($) Equally Likely Construct Large Plant 200, ,00010,000 Construct Small Plant 100,000-20,00040,000 Do Nothing000 Probabilities0.5

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Decision Making Under Uncertainty Criterion of Realism (Hurwicz): CR = *(row max) + (1- )*(row min) =0.8 States of Nature Favorable Mkt ($) Unfavorable Mkt ($) CR Construct Large Plant 200, ,000124,000 Construct Small Plant 100,000-20,00076,000 Do Nothing000

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Decision Making Under Uncertainty Minimax - choose the alternative with the minimum maximum Opportunity Loss - this is using EOL table States of Nature Favorable Mkt ($) Unfavorable Mkt ($) Minimax Regret Construct Large Plant 0180,000 Construct Small Plant 100,00020,000 Do Nothing200,0000 Probabilities0.5

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Summary Decision theory Decision Making under Risk Decision Making under Uncertainty

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