2. Introduction
Our decision analyses in Chapter 4R primarily discussed
consequences or payoff in terms of monetary value.
Using probability information about the outcomes of chance events,
we deemed the best decision as the one with the best payoff.
But what about decisions that need to take into account other
intangibles such as risk, public view, etc?
The long term view of Wall Street firms is a great example of this.
This leads to the definition of utility.
This chapter looks at two (separate) topics: The meaning of utility
and game theory.
3. Utility
Definition : The total worth of a particular outcome; it reflects the decision
maker's attitude toward a collection of factors such as profit, loss, and risk.
Utility becomes extremely important as payoffs become extreme and/or there
is an increased exposure to downside risk.
The book gives a great example of Atlanta-based Swofford Real Estate.
Using a pure EV approach, decision alternative 1 looks clearly like the best
alternative.
But if Swofford can't afford to lose even 30K because it might drive the
company out of business -- then d3 is the only way to go.
This possible extreme consequence factors into our utility that we can use to
factor into monetary outcomes to make optimal decisions.
4. Utility and Decision Making
If we are strictly talking about the utility of money, we can use the following
steps
Use the following step to follow the example on pages 155-158 .
Steps:
1. Develop a payoff table using monetary values
2. Identify the best and worst payoff values in the table and assign
each a utility value, with U(best payoff) > U(worst payoff)
3. For every other monetary value M in the original payoff table, do
the following to determine its utility value
a. Define the lottery: The best payoff is obtained with the
probability p. Worst payoff (1-p)
b. Determine the value of p such that the decision maker is
indifferent between a guaranteed payoff M and the lottery
defined in step 3(a).
c. Calculate the utility of M as follows:
U(M) = pU(best payoff) + (1-p)U(worst payoff)
4. Convert the payoff table from monetary values to utility values.
5. Apply the expected utility approach to the utility table from step 4 and select the decision
alternative with the highest expected utility.
5. Utility: Other Considerations
Risk Avoiders v. Risk Takers
In the case of Swofford, our president was viewed as a risk avoider.
Hence decision 3 (no investment) became the best alternative.
A risk taker is one who would choose the lottery over a better
guaranteed payoff.
Hence decision 2 might be a better alternative in this case (see p.
161)
We can also have a risk neutral decision maker
The following slide shows the utility functions for each type of
decision maker.
6. Utility: Other Considerations
If risk neutral - monetary value and utility value will always lead to identical recommendations.
If our decision maker is risk neutral, the trick lies in finding a risk neutral range that yields the highest payoff
within that range.
We have to do our best to assess levels of reasonableness, then the decision with the best monetary value can be
used.
7. End of Part I of Chapter 5R
Read the section.
Do the problems
On to Game Theory!
8. Game Theory
In decision analysis, a decision maker seeks an optimal decision after
considering the possible outcomes of one or more chance events.
In game theory , two or more decision makers are called players and
compete as adversaries against each other.
Each player selects a strategy independent of knowledge of the other
players strategy.
In this section we discuss two-person zero sum games -- where the
gain for one is equal to the loss of the other.
9. Game Theory
Example: Competing for Market Share
What are the optimal strategies for the two companies.
Company A uses a maximin approach, while Company B uses a minimax approach.
A pure strategy is defined as when the maximin = minimax.
