MBA201a: Decision Analysis
Decision tree basics: begin with no uncertainty
Basic setup:
Example: deciding where to eat
lunch
– Trees run left to right
chronologically.
Japanese
– Decision nodes are
represented as squares.
Greek
– Possible choices are
represented as lines (also
called branches).
North Side
Burritos
South Side
Thai
Professor Wolfram
– The value associated with
each choice is at the end of
the branch.
MBA201a - Fall 2009
Page 1
Assigning values to the nodes involves defining goals.
Example: deciding where to eat
lunch
Taste
versus
Speed
Japanese
4
1
3
2
1
4
2
3
North Side
Greek
Burritos
South Side
Thai
Professor Wolfram
MBA201a - Fall 2009
Page 2
To solve a tree, work backwards, i.e. right to left.
Example: deciding where to eat
lunch
Speed
Japanese
1
North Side
Value =2
Greek
2
Value =4
Burritos
South Side
Value =4
Thai
Professor Wolfram
4
3
MBA201a - Fall 2009
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Decision making under uncertainty
Example: a company deciding whether
to go to trial or settle a lawsuit
Win [p=0.6]
Go to trial
– Chance nodes are
represented by circles.
– Probabilities along each
branch of a chance node
must sum to 1.
Lose [p= ]
Settle
Professor Wolfram
MBA201a - Fall 2009
Page 4
Solving a tree with uncertainty:
Win [p=0.6]
Go to trial
-$.5M
$0
EV=
-$8M
-$4M
– We’re assuming the decisionmaker is maximizing expected
values.
Settle
Professor Wolfram
pwinx win payoff + plosex lose payoff
– In this tree, “Go to trial” has a
cost associated with it that
“Settle” does not.
Lose [p=0.4]
EV=
– The expected value (EV) is the
probability-weighted sum of the
possible outcomes:
MBA201a - Fall 2009
Page 5
Decision tree notation
Chance nodes
(circles)
Expected value of
chance node (or
certainty equivalent)
Probabilities
(above the branch)
Win [p=0.6]
$0
Go to trial
-$3.7M
-$.5M
EV= -$3.2M
Lose [p=0.4]
Decision nodes
(squares)
-$8M
EV= -$3.7M
Settle
Professor Wolfram
-$8.5M
-$4m
-$4M
Value of optimal
decision
-$.5M
Terminal values
corresponding to
each branch (the
sum of payoffs
along the branch).
-$4M
Running total
of net expected
payoffs
(below the branch)
Payoffs
(below the branch)
MBA201a - Fall 2009
Page 6
Decision analysis & decision trees
Why is decision analysis a useful tool?
– The process of doing the analysis, i.e. writing down a
decision tree, forces you to make explicit what your goals
are, what elements are within your control, and what risks
are outside your control.
– It keeps you from getting confused when there are
contingent decisions.
– It helps you figure out when gathering more information will
be valuable.
The basic idea: look forwards, reason backwards.
Decision trees are the tool used to do decision analysis.
Professor Wolfram
MBA201a - Fall 2009
Page 7