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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 can’t 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**

Clearly define the problem at hand List the possible alternatives Identify the possible outcomes & criteria List the payoff or profit of each combination of alternatives and outcomes Select one of the mathematical decision theory models 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**

Expected Monetary Value: (Sum of the probabilities and outcome) n nature, of states number the to 1 j where ) P(S * Payoff i) ative EMV(Altern S = å

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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 Alternative Good Economy Poor Economy Portfolio 1 (high risk) 80 -20 Portfolio 2 (med risk) 30 20 Portfolio 3 (low risk) 23 Probability 0.3 0.7 Which portfolio should you invest in, that will maximize your returns?

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Decision Table State Of Nature Decision Alternative Good Economy Poor Economy EMV Portfolio 1 (high risk) 80 -20 10 Portfolio 2 (med risk) 30 20 23 Portfolio 3 (low risk) 22 Probability 0.3 0.7 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 places an upper bound on what one would pay for additional information EVPI is the expected value with perfect information minus the maximum EMV EVPI = EV|PI - maximum EMV

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**EVPI = Expected Value with Perfect Information - max(EMV) =**

State Of Nature Decision Alternative Good Economy Poor Economy EMV Portfolio 1 (high risk) 80 -20 Portfolio 2 (med risk) 30 20 23 Portfolio 3 (low risk) 22 Probability 0.3 0.7 EVPI = Expected Value with Perfect Information - max(EMV) = [80 0.7] – 23 = $16.4

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**Expected Opportunity Loss**

EOL is the cost of not picking the best solution 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 Alternative Good Economy**

Poor Economy EOL Portfolio 1 (high risk) 80 – 80 = 0 22 – (-20) = 42 Portfolio 2 (med risk) 80 – 30 = 50 22 – 20 = 2 Portfolio 3 (low risk) 80 – 22 = 58 22 – 22 = 0 Probability 0.3 0.7

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**EOL Table State Of Nature Decision Alternative Good Economy**

Poor Economy EOL Portfolio 1 (high risk) 42 29.4 Portfolio 2 (med risk) 50 2 16.4 Portfolio 3 (low risk) 58 17.4 Probability 0.3 0.7

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**Sensitivity Analysis EMV(high risk) = $80P + (-$20) (1-P)**

EMV(med risk) = $30P + $20(1-P) EMV(low risk) = $22P + $22(1-P)

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**Sensitivity Analysis - continued**

0.444 0.2 EMV (Med Risk) EMV(low Risk) EMV(High 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 200,000 -180,000 Construct Small Plant 100,000 -20,000 Do Nothing

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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 -180,000 -18,000 Construct Small Plant 100,000 -20,000 Do Nothing

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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 200,000 -180,000 10,000 Construct Small Plant 100,000 -20,000 40,000 Do Nothing Probabilities 0.5

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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 200,000 -180,000 124,000 Construct Small Plant 100,000 -20,000 76,000 Do Nothing

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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 180,000 Construct Small Plant 100,000 20,000 Do Nothing 200,000 Probabilities 0.5

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**Summary Decision theory Decision Making under Risk**

Decision Making under Uncertainty

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