Decision Theory: Session 1: Decision Problem No. 1

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Decision Theory Session 1 Decision Problem No. 1

• General Description of the Problem
• Unidentified airplane enters secured airspace,
  and is approaching a top secret intelligence
  installation.

• The airplane may be a strayed civilian airplane,
  carrying civilian passengers, a military aircraft
  on a reconnaissance mission, out to photograph
  the intelligence installation, or a bomber sent
  to bomb and destroy the installation.

• The implications of any of these possibilities
  are as follows

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The Airplane ProblemEvents, Actions and
Implications

• Type of Plane Action Taken Outcome Consequence
• Civilian None Flies away safely None
• Civilian Fire Missile Innocent Civilians Internati
  onal outrage, killed need to pay huge
  com- pensation to families and
  neighbor state
• Recon None Installations Need to move
  secrets exposed installation to another
  location
• Recon Fire Missile Destroyed None Intelli
  gence threat to Installation
• Bomber None Destroy Installation Casualties,
  replacement cost, internal
  criticism
• Bomber Fire Missile Eliminate threat
  to None installation

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The Airplane Problem Generic Decision Tree
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The Airplane Problem Probability Estimates
Civilian Plane
Do Nothing
Recon Plane
Bomber
Civilian Plane
Recon Plane
Miss
Bomber
Fire Missile
Civilian Plane
Recon Plane
Hit
Bomber
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The Airplane Problem Monetary Value Assessments
Civilian Plane
0.5
Do Nothing
Recon Plane
0.3
0.2
Bomber
Civilian Plane
0.5
Recon Plane
Miss
0.3
0.15
0.2
Bomber
Fire Missile
Civilian Plane
-100,000,000
0.5
0.85
Recon Plane
0.3
Hit
0.2
Bomber
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The Airplane Problem Expected Value Analysis
EVDN 0 ? 0.5 (-10,000,000) ? 0.3
(-50,000,000) ? 0.2 -13,000,000
Civilian Plane
0.5
Do Nothing
Recon Plane
0.3
Bomber
0.2
Civilian Plane
0.5
Recon Plane
Miss
0.3
0.15
0.2
Bomber
Civilian Plane
Fire Missile
0.5
Recon Plane
0.85
0.3
Hit
0.2
Bomber
EVFM 0.85 ? -100,000,000 ? 0.5 0 ? 0.3
0 ? 0.2 0.15 ? 0.5 (-10,000,000) ?
0.3 (-50,000,000) ? 0.2 -44,500,000
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The expected value of Alternative i, Evi is
given by
Where pi is the probability of the ith outcome
and vi is the utility of the ith outcome for an
alternative with a total of na outcomes.

• Conditions on probability and outcomes
• Mutual Exclusiveness Oi ?Oj ? and pi ? pj
  pi? pj, for all j?i,
• Logical Exhaustiveness

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