Do TPD08.docx

[Tutorial G05] Decision theory

§ G05.1 Introduction

Decision theory might be considerd to be a branch of mathematics. It provides a more precise and systematic study of the formal or abstract properties of decision-making scenarios. Game theory concerns situations where the decisions of more than two parties are involved. Decision theory considers only the decisions of a single individual. Here we discuss only some very basic aspects of decision theory.

The decision situations we consider are cases where a decision maker has to choose between a list of mutually exclusive decisions. In other words, from among the alternatives, one and only one choice can be made. Each of these choices might have one or more possible consequences that are beyond the control of the decision maker, which again are mutually exclusive.

Consider an artificial example where someone, say Linda, is thinking of investing in the stock market. Suppose she is considering four alternatives : investing $8000, investing $4000, investing $2000, or not investing at all. These are the four choices that are within her control. The consequences of her investment, in terms of her profit or loses, are dependent on the market and beyond her control. We might draw up a payoff table as follows :

Although the possible returns of the investment are beyond the control of the decision maker, the decision maker might or might not be able or willing to assign probabilities to them. If no probabilities are assigned to the possible consequences, then the decision situation is called "decision under uncertainty". If probabilities are assigned then the situation is called "decision under risk". This is a basic distinction in decision theory, and different analyses are in order.

§ G05.2 Decision under uncertainty

Maximin

The Maximin decision rule is used by a pessimistic decision maker who wants to make a conservative decision. Basically, the decision rule is to consider the worst consequence of each possible course of action and chooses the one thast has the least worst consequence.

Applying this rule to the payoff table above, the...