Jessie
Jumpshot
15.067 Fall 2005
1
Common Mistakes
• Forgetting to deduct the agent’s salary from Jessie’s total
package
• Failing to calculate certainty equivalents
– I.E.
$12M*10%ProbabilityWin + $2M*90%ProbabilityLose
= CE[Sharks Merchandising Profit] = $3M
– CE[Sharks:20% merchandizing profit if win] = $1.2M*0.20
= $240,000
– Where $12M * 10% = $1.2M
• Teammates writing down “different deals”
– When differences occurred, I went with the majority
2
Histogram of Salary Range
Number of Students
Histogram - Range of Salaries
9
8
7
6
5
4
3
2
1
0
1M - 1.9M
2.1M
2.2M-2.49M
Salary Range
3
2.5M-2.9M
3M+
Histogram of Bonus Range
Range of Bonus
Expected Value to Jessie
4
3
2
1
0
Less than 300K
500K - 1M
1M - 2M
Greater than 2M
Range
Range of Bonus
Expected Value to Sharks
Number of Students
Number of Students
5
5
4
3
2
1
0
Less than 100K
100-200K
300-400K
Range
4
Greater than 400K
Histogram of Jessie’s Total Value
Total Dollar Values for Jessie
Number of Students
6
4
2
0
$2.5M$3.0M
$3.0M$3.5M
$3.5M$4.0M
$4.0M$5.0M
Total $ Values
5
$5.0M$5.5M
$6M+
Histogram of Shark’s Total Costs
Number of Students
Histogram - Sharks Total Cost
9
8
7
6
5
4
3
2
1
0
$1.0M-$2.5M
$2.5M-$3.0M
$3.0M-$3.5M
Total Cost
6
$3.5M-$4.0M
Comparing Jessie vs Shark Net Gains
Sharks vs. Jessie's Net Gains
18,000,000
Jessie’s Best,
Sharks Worst
16,000,000
14,000,000
Jessie's Net Gains
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
Jessie’s Worst,
Sharks Best
2,000,000
0
($1,000,000)
($500,000)
$0
$500,000
$1,000,000
Sharks Net Gain
7
$1,500,000
$2,000,000
$2,500,000
$3,000,000
Jessie Z-Score Calculation
Jessie
Average Net Gain: $2,200,038
Standard Dev: $1,734,676
Jessie’s NET GAIN = [(.95)Salary+.6Win(Merchandise Profit)
+.4Don’t(Merchandise Profit) + .6Win(Bonus) + .4Don’t(Bonus)] – $2.1M
Jessie’s Z-score = ([Jessie’ NET GAIN-Avg(Jessie Net Gain)] /([Jessie
StDev Net Gain])
Notice: Jessie’s Certainty Equivalent assumes she will win 60% of the time
and not win 40% of the time
Average Final Agreement: $4,558,866
8
Agent Z-Score Calculation
Agent
Average Commission: $118,080 Standard Dev: $23,293
Agent’s NET GAIN = .05(Salary) – Average Commission
Agent’s Z-score = ([Agent’s NET GAIN] /([Agent’s StDev])
Notice: Agent’s Certainty Equivalent is fixed at 5% of Jessie’s salary
9
Sharks Z-Score Calculation
Sharks Manager
Average Net Gain: $58,824 Standard Dev: $543,109
Manager’s NET GAIN = $3M - [Salary+.1Win(Merchandise Profit)
+.9Don’t(Merchandise Profit) + .1Win(Bonus) + .9Don’t(Bonus)]
Manager’s Z-score = ([Manager’s’ NET GAIN-Avg(Manager Net Gain)]
/([Manager StDev])
Notice: Manager’s Certainty Equivalent assumes Jessie will win 10% of the
time and not win 90% of the time
Average Final Cost: 2,933,333
10
MIT OpenCourseWare
http://ocw.mit.edu
15.067 Competitive Decision-Making and Negotiation
Spring 2011
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