Using the payoff table of Worked Example 6, with $P(S_1)=0.3$, $P(S_2)=0.5$, $P(S_3)=0.2$, compute the Expected Monetary Value (EMV) of each course of action and state which should be chosen. Also compute the Expected Opportunity Loss (EOL) of each action and verify that it points to the same choice.

**EMV calculation**, using the payoff table $A_1=(200,200,200)$, $A_2=(100,300,300)$, $A_3=(50,200,400)$ and probabilities $P(S_1)=0.3,P(S_2)=0.5,P(S_3)=0.2$: $$EMV(A_1)=200(0.3)+200(0.5)+200(0.2)=60+100+40=200$$ $$EMV(A_2)=100(0.3)+300(0.5)+300(0.2)=30+150+60=240$$ $$EMV(A_3)=50(0.3)+200(0.5)+400(0.2)=15+100+80=195$$ Highest EMV is $A_2$ (240) → **choose $A_2$**. **EOL calculation**, using the regret table from Worked Example 6 — $A_1=(0,100,200)$, $A_2=(100,0,100)$, $A_3=(150,100,0)$ — with the same probabilities: $$EOL(A_1)=0(0.3)+100(0.5)+200(0.2)=0+50+40=90$$ $$EOL(A_2)=100(0.3)+0(0.5)+100(0.2)=30+0+20=50$$ $$EOL(A_3)=150(0.3)+100(0.5)+0(0.2)=45+50+0=95$$ Lowest EOL is $A_2$ (50) — the **same** action EMV recommended. …

Using the payoff table of Worked Example 6, with P(S₁)=0.3, P(S₂)=0.5, P(S₃)=0.2, compute the Expected Monetar

Worked Examples · Example 14

P(S_1)=0.3

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Concept understanding — Decision-Making under Risk (EMV and EOL)

When the probabilities of the states of nature are known, the Expected Monetary Value (EMV) criterion picks the action with the highest probability-weighted average payoff. The equivalent Expected Opportunity Loss (EOL) criterion picks the action with the lowest probability-weighted average regret, and always agrees with EMV. The Expected Value of Perfect Inf …

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Concept understanding — Decision-Making under Risk (EMV and EOL)

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