Fundamentals of Decision Theory Models

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?

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.

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

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

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)

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

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…

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?

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?

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

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  0.3 + 22  0.7] – 23 = $16.4

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.

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

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

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

Sensitivity Analysis - continued 0.444 0.2 EMV (Med Risk) EMV(low Risk) EMV(High Risk)

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

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

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

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

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

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

Summary Decision theory Decision Making under Risk Decision Making under Uncertainty