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Decision Theory: Session 1: Decision Problem No. 1

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.

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Decision Theory: Session 1: Decision Problem No. 1

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  1. 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:

  2. The Airplane Problem:Events, Actions and Implications • Type of PlaneAction TakenOutcomeConsequence • Civilian None Flies away safely None • Civilian Fire Missile Innocent Civilians International outrage, killed need to pay huge com- pensation to families and neighbor state • Recon None Installation’s Need to move secrets exposed installation to another location • Recon Fire Missile Destroyed None Intelligence threat to Installation • Bomber None Destroy Installation Casualties, replacement cost, internal criticism • Bomber Fire Missile Eliminate threat to None installation

  3. The Airplane Problem: Generic Decision Tree Civilian Plane Recon Plane Do Nothing Bomber Civilian Plane Miss Recon Plane Bomber Fire Missile Civilian Plane Recon Plane Hit Act Fork Bomber Event Fork

  4. The Airplane Problem: Probability Estimates 0.5 0.3 0.2 0.5 0.3 0.15 0.2 0.5 0.85 0.3 0.2 Civilian Plane Do Nothing Recon Plane Bomber Civilian Plane Miss Recon Plane Bomber Fire Missile Civilian Plane Recon Plane Hit Bomber

  5. The Airplane Problem: Monetary Value Assessments $0 -$10,000,000 -$50,000,000 $0 -$10,000,000 -$50,000,000 $0 $0 Civilian Plane 0.5 Do Nothing Recon Plane 0.3 0.2 Bomber Civilian Plane 0.5 Miss Recon Plane 0.15 0.3 0.2 Bomber Fire Missile Civilian Plane -$100,000,000 0.5 0.85 Recon Plane 0.3 Hit 0.2 Bomber

  6. The Airplane Problem: Expected Value Analysis $0 -$10,000,000 -$50,000,000 $0 -$10,000,000 -$50,000,000 -$100,000,000 $0 $0 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 0.2 Bomber Civilian Plane 0.5 Miss Recon Plane 0.15 0.3 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  0.5 + (-10,000,000)  0.3 + (-$50,000,000)  0.2 ] = -$44,500,000

  7. The expected value of Alternative i, Evi is given by: Where piis the probability of the ith outcome and viis 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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