Editing Decision tree (section)

=== Analysis example ===
Analysis can take into account the decision maker's (e.g., the company's) preference or [[utility function]], for example:

[[Image:RiskPrefSensitivity2Threshold.png|center]]

The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $400K—in that range of risk aversion, the company would need to model a third strategy, "Neither A nor B").

Another example, commonly used in [[operations research]] courses, is the distribution of lifeguards on beaches (a.k.a. the "Life's a Beach" example).<ref>{{Cite book|title=Principles of Operations Research: With Applications to Managerial Decisions|last=Wagner|first=Harvey M.|date=1975-09-01|publisher=Prentice Hall|isbn=9780137095926|edition=2nd|location=Englewood Cliffs, NJ|language=English|url-access=registration|url=https://archive.org/details/principlesofoper00wagn}}</ref> The example describes two beaches with lifeguards to be distributed on each beach. There is maximum budget ''B'' that can be distributed among the two beaches (in total), and using a marginal returns table, analysts can decide how many lifeguards to allocate to each beach.
{| class="wikitable"
|+
!Lifeguards on each beach
!Drownings prevented in total, beach #1
!Drownings prevented in total, beach #2
|-
|1
|3
|1
|-
|2
|0
|4
|}
In this example, a decision tree can be drawn to illustrate the principles of [[diminishing returns]] on beach #1.
[[File:Beachdecisiontree.png|alt=|none|thumb|Beach decision tree]]

The decision tree illustrates that when sequentially distributing lifeguards, placing a first lifeguard on beach #1 would be optimal if there is only the budget for 1 lifeguard. But if there is a budget for two guards, then placing both on beach #2 would prevent more overall drownings.
[[File:Lifeguards.png|thumb|Lifeguards|alt=|center]]