Transcript UNFAVORABLE MARKET

Decision Analysis
© 2008 Prentice-Hall, Inc.
Decision Trees
 Any problem that can be presented in a
decision table can also be graphically
represented in a decision tree
 Decision trees are most beneficial when a
sequence of decisions must be made
 All decision trees contain decision points
or nodes and state-of-nature points or
nodes
 A decision node from which one of several
alternatives may be chosen
 A state-of-nature node out of which one state
of nature will occur
© 2009 Prentice-Hall, Inc.
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Five Steps to
Decision Tree Analysis
1. Define the problem
2. Structure or draw the decision tree
3. Assign probabilities to the states of
nature
4. Estimate payoffs for each possible
combination of alternatives and states of
nature
5. Solve the problem by computing
expected monetary values (EMVs) for
each state of nature node
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Structure of Decision Trees
 Trees start from left to right
 Represent decisions and outcomes in
sequential order
 Squares represent decision nodes
 Circles represent states of nature nodes
 Lines or branches connect the decisions
nodes and the states of nature
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Each chance node must have branches that correspond
to a set of mutually exclusive and collectively
exhaustive outcomes.
Two outcomes are mutually exclusive (or disjoint) if the
occurrence of one of the outcomes precludes the
simultaneous occurrence of the other.
If you make a list of the outcomes which can occur when
you adopt a particular course of action then this list is said
to be exhaustive if your list includes every possible
outcome.
© 2008 Prentice-Hall, Inc.
Double-Risk Dilemma
 Assume that you have a ticket that will let you
participate in a game of chance (a lottery) that will
pay off $10 with a 45% chance (or a 55% chance
of nothing).
 Your friend has a ticket to a different lottery that
has a 20% chance of paying $25 (or an 80%
chance of nothing).
 Your friend has offered to let you have his ticket if
you will give him your ticket plus $1.
 Should you agree to the trade and play to win
$25, or should you keep your ticket?
© 2009 Prentice-Hall, Inc.
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Max Profit
EMV=
$4 EMV=
Trade Ticket
$4
Trade
-$1 Ticket
-$1
EMV=
$4.5
EMV=EMV=
$4.5 $4.5
Win (0.20)
$25Win (0.20)
Max$24
Profit
$25
Lose (0.80)
$0 Lose (0.80)
$0
Win (0.45)
Win (0.45)
$10$10
$24
=EMV
=EMV
-$1
$10
$10
$0
(0.55)
LoseLose
(0.55)
$0 $0
$4.00
-$1
Keep Ticket
Keep Ticket
$0
y
Pr(Y=y) y*Pr(Y=y)
$24.00
0.2
$4.80
y
Pr(Y=y) y*Pr(Y=y)
-$1.00
0.8
-$0.80
$24.00
0.2
$4.80
$4.00
-$1.00
0.8
-$0.80
$0
$0
yy
$10.00
$10.00
$0.00
$0.00
Pr(Y=y) y*Pr(Y=y)
y*Pr(Y=y)
Pr(Y=y)
0.45
$4.50
0.45
$4.50
0.55
$0.00
0.55
$0.00
$4.50
$4.50 =EMV=EMV
© 2009 Prentice-Hall, Inc.
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Thompson Lumber Company
STATE OF NATURE
ALTERNATIVE
FAVORABLE
MARKET ($)
UNFAVORABLE
MARKET ($)
Construct a large plant
200,000
–180,000
Construct a small plant
100,000
–20,000
0
0
Do nothing
Table 3.1
© 2009 Prentice-Hall, Inc.
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Thompson’s Decision Tree
A State-of-Nature Node
Favorable Market
A Decision Node
1
Unfavorable Market
Favorable Market
Construct
Small Plant
2
Unfavorable Market
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Thompson’s Decision Tree
EMV for Node
1 = $10,000
= (0.5)($200,000) + (0.5)(–$180,000)
Payoffs
Favorable Market (0.5)
Alternative with best
EMV is selected
1
Unfavorable Market (0.5)
Favorable Market (0.5)
Construct
Small Plant
2
Unfavorable Market (0.5)
EMV for Node
2 = $40,000
$200,000
–$180,000
$100,000
–$20,000
= (0.5)($100,000)
+ (0.5)(–$20,000)
$0
© 2009 Prentice-Hall, Inc.
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Texaco vs. Pennzoil
• In early 1984, Pennzoil and Getty Oil agreed to the
terms of a merger. But before any formal documents
could be signed, Texaco offered Getty Oil a
substantially better price.
• Getty Oil agreed and sold to Texaco.
• In 1985, Pennzoil filed a lawsuit against Texaco. And
won the case…awarded $11.0 billion.
• Texaco appealed ----- court  $10.3 billion.
• Texaco threat to file for bankruptcy if Pennzoil secured
the judgment.
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• In 1987, Texaco offered to pay Pennzoil $2billion to
settle the case.
• Pennzoil chairman indicated that a settlement between
$2 and $5 billion would be fair.
Should Pennzoil accepts or refuses and make a
counteroffer of $5billion?
Texaco Might
1- Accepts to pay $5 billion
2- Refuses and counteroffer of $3 billion
3- Refuses and goes to court
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
2
Texaco Accepts $5 Billion (0.17)
5
High (0.20)
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
Final Court
Decision
Medium (0.50)
Low (0.30)
High (0.20)
Refuse
Final Court
Decision
Medium (0.50)
Low (0.30)
Texaco
(0.33)
Counter offers $3 Billion
Accept $3 Billion
10.3
5
0
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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High (0.20)
Final Court
Decision
Medium (0.50)
Low (0.30)
Step 1
10.3
5
0
y
10.300
5.000
0.000
Pr(Y=y)
0.2
0.5
0.3
y*Pr(Y=y)
$2.06
$2.50
$0.00
$4.56
=EMV
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
2
Texaco Accepts $5 Billion (0.17)
EMV =
4.56
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
5
High (0.20)
Final Court
Decision
Medium (0.50)
Low (0.30)
EMV =
4.56
Refuse
High (0.20)
Final Court
Decision
Medium (0.50)
Low (0.30)
Texaco
(0.33)
Counter offers $3 Billion
Accept $3 Billion
10.3
5
0
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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High (0.20)
EMV=
4.56
Refuse
EMV=
4.56
Final Court
Decision
Medium (0.50)
Low (0.30)
Accept $3 Billion
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
2
Texaco Accepts $5 Billion (0.17)
EMV =
4.56
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
5
High (0.20)
Final Court
Decision
Medium (0.50)
Low (0.30)
High (0.20)
EMV =
4.56
Refuse
Final Court
Decision
Medium (0.50)
Low (0.30)
Texaco
(0.33)
Counter offers $3 Billion
Accept $3 Billion
10.3
5
0
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
Max2Result
Accept $2 Billion
2
Texaco Accepts $5 Billion (0.17)
Texaco Accepts $5 Billion (0.17)
5
5
EMV=
EMV=
EMV=
EMV=
4.63
4.56
4.63
Counteroffer
Texaco Refuses (0.50)4.56
Counteroffer
Texaco Refuses (0.50)
$5 Billion
$5 Billion
y
Pr(Y=y)
y*Pr(Y=y)
y
Pr(Y=y) y*Pr(Y=y)
5.000
5.000
0.170.17 $0.85 $0.85
4.560
4.560 0.5 0.5 $2.28 $2.28
4.560
4.560 0.330.33 $1.50 $1.50
$4.63
=EMV
$4.63
=EMV
Counteroffer
Counteroffer
Texaco
Counter offers $3 Billion
Texaco
Counter offers $3 Billion
(0.33)
(0.33)
EMV=
4.56
EMV=
4.56
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
2
EMV=
4.63
Counteroffer
$5 Billion
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Decision Path: A path starting at the left most node up
to the values at the end of a branch by selecting one
alternative from a decision node or by following one
outcome from uncertainty nodes.
Decision Strategy: The collection of decision paths
connected to a branch of the left most node by selecting
one alternative from each decision node along these
paths.
Optimal Decision Strategy: That Decision Strategy
which results in the highest EMV if we maximize profit
and the lowest EMV if we minimize cost.
© 2009 Prentice-Hall, Inc.
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Max Result
Accept $2 Billion
2
EMV=
4.63
Texaco Accepts $5 Billion (0.17)
EMV=
4.63
High (0.20)
EMV=
4.56
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
Final Court
Decision
Medium (0.50)
Low (0.30)
High (0.20)
EMV=
4.56
EMV=
4.56
5
Refuse
Final Court
Decision
Medium (0.50)
Low (0.30)
Texaco
(0.33)
Counter offers $3 Billion
Accept $3 Billion
10.3
5
0
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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D1 =“Accept 2 Billion”
Accept $2 Billion
2
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D2 = “Counter 5 Billion, Refuse Counter of $3
Billion”
Texaco Accepts $5 Billion (0.17)
5
High (0.20)
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
Final Court
Decision
Medium (0.50)
Low (0.30)
High (0.20)
Refuse
Texaco
(0.33)
Counter offers $3 Billion
Final Court
Decision
Medium (0.50)
Low (0.30)
10.3
5
0
10.3
5
0
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D3 = “Counter 5 Billion, Accept $3
Billion”
Texaco Accepts $5 Billion (0.17)
High (0.20)
Counteroffer
Texaco Refuses (0.50)
$5 Billion
Counteroffer
(0.33)
Texaco
Counter offers $3 Billion
Final Court
Decision
Medium (0.50)
Low (0.30)
Accept $3 Billion
5
10.3
5
0
3
© 2009 Prentice-Hall, Inc.
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OPTIMAL DECISION STRATEGY
Counteroffer $5 Billion.
Next, if Texaco Counteroffers
$3 Billion, refuse the counteroffer.
Number of Decision Strategies in Decision
Tree above: 3
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