Decision Analysis
Decision analysis compares alternatives under uncertainty using a payoff table, decision criteria, and expected values. STPM 950 tests maximax, maximin, minimax regret, expected monetary value (EMV), decision trees, and the expected value of perfect information (EVPI).
Criteria
- Maximax: choose the alternative with the highest possible payoff (optimistic).
- Maximin: choose the alternative whose worst payoff is best (pessimistic).
- Minimax regret: build a regret table (best payoff in each state minus each payoff), then minimise the maximum regret.
- EMV: multiply payoffs by state probabilities and sum; choose the highest EMV.
EVPI = expected payoff with perfect information − maximum EMV. It is the most you should pay for perfect information.
Worked example: A1 pays 120 in a good state and −30 in a bad state; A2 pays 70 and 40. P(good)=0.6, P(bad)=0.4. EMV(A1)=0.6(120)+0.4(−30)=60; EMV(A2)=0.6(70)+0.4(40)=58, so choose A1. Perfect information value = 0.6(120)+0.4(40)=88; EVPI=88−60=28. Maximin chooses A2 (worst payoffs −30 vs 40). Minimax regret: regrets A1=0,70; A2=50,0; maximum regrets 70 and 50, so choose A2.
Traps: mixing maximin with minimax; computing EVPI as the perfect-information payoff alone; forgetting that probabilities must sum to 1; and reversing rows in the regret table.