Week 5 - Decision Making Under Uncertainty

What must we identify before we start decision making under uncertainty?

- Decision Alternatives - States of Nature - Pay-off for each decision alternative and state of nature - What I value in my decision?

Define Decision Types: Risky Decisions

Certain values have probabilistic outcomes, but the distribution of the probability is known. For example, demand for a product with a long history

Define Decision Types: Uncertain Decisions

Certain values have unknown or random outcomes and we have no information of the distribution that drives the outcome. For example, demand for a completely new product

Define Decision Types: Competitive Decisions

Decisions taken in an environment where the outcome of the decision depends on the (simultaneous thus unknown) choices by somebody else

What are the critiques of decision making under uncertainty?

Five of the criteria are irrational as they all (except the Laplace) ignore most of the available information in the payoff matrix

Define an Optimist

Someone who believes that the best will always happen

Define an Pessimist

Someone who believes the worst will always happen

Define a Sore loser

Someone who makes decision so as avoid the regret of making the wrong decision

Define a Calculator

Someone who will methodically gathers data and evidence and chooses the mathematically best option

Define Decision Types: Certain Decisions

Values (such as costs, capacity, no. of employees) that describe a situation are known

What is included in the decision-making process

• Define the problem • Identify the set of alternatives • Determine the criteria for making a decision • Evaluate the alternatives using the criteria • Choose the alternative

What are decision tables?

•Decision tables are useful when you can list -All possible strategies or decisions are -All random outcomes or scenarios, and their probabilities -The payoff (e.g. profit) for each decisions and scenario •and only a single decision is made •and the probabilities for the state of nature is the same for each decision choice. •It is then easy to determine the best alternative under a given decision rule

What are the Decision Rules (1 of 3) for decision making under risk?

•Expected monetary value (EMV): Make a decision that maximises the EMV (applied to a payoff matrix), use equation Expected regret or opportunity loss (EOL): Make a decision that minimises the EOL (applied to a regret matrix, use equation

What are the Decision Rules (2 of 3) for decision making under risk?

•Expected value of perfect information (EVPI) -Suppose we could hire a consultant who could predict the future with 100% accuracy -With such perfect information we could make each decision that maximise the payoff: Expected Profit of a Perfect Predictor (EPPP) •EPPP = Sum of the product of the highest profit and probability of each state of nature use euqation -EVPI is the maximum amount of money we are willing to pay to improve our knowledge of the future

What are the Decision Rules (3 of 3) for decision making under uncertainty?

•Hurwitz. Select a co-efficient of optimism, . If you are very optimistic about the future then select near 1, pessimistic, select near 0. The rank each option with Hurwicz payoff, H = ax(maximum payoff) + (1-a)x(minimum payoff) •Maximum Likelihood. Choose the option with the highest pay-off for the state of nature that is deemed most likely to occur.

What are the Decision Rules (2 of 3) for decision making under uncertainty?

•Laplace. Determine the average payoff for each option and choose the alternative with the best average benefit. Assume that each of the states of nature are equally as probable. The logical/mathematical choice •Minimax. Identify the possible 'regret' or 'opportunity loss' for each alternative under each state of nature and choose the alternative with the smallest maximum regret (the "best worst" regret). Sore losers try to minimise the lost opportunity from making the wrong decision Regret = (The best payoff under the given state of nature) - (The actual payoff for the given alternative under the same state of nature)

What are the Decision Rules (1 of 3) for decision making under uncertainty?

•Maximax. Determine the best possible payoff for each scenario and choose the alternative with the highest maximum payoff. An optimistic approach, but high losses that are risked in order to access the highest payoff are completely ignored •Maximin. Determine the worst possible payoff for each scenario and choose the "best worse" alternative with the largest minimum payoff. A pessimistic (conservative) approach that maximises the "guaranteed minimum return". Risk adverse to minimise damage

How to do the Hurwitz Criterion

•Select a "co-efficient of optimism", 0 < α < 1. If you are very optimistic about the future then select α near 1, pessimistic, select α near 0. Then you rank each option with Hurwicz Payoff euqation

What are the critiques of the expected value approach

•The expected value world-view is long term one. -Expected value is the average pay-off after an infinite number of trails of the experiment. -Many decisions are made only once and thus the expected value operator may not be the best selection criterion, especially if the decision is being taken by a small company that may not be able to afford to make a wrong decision.