Decision theory introductory problem
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The document discusses decision-making under risk for an electrical goods merchant selling electric irons, detailing various strategies regarding stock purchase and potential demand scenarios. It presents payoff and opportunity loss tables, expected monetary value (EMV) calculations for different strategies, and decision criteria to optimize profit margins. The analysis aids in determining the best purchasing strategy while factoring in uncertainty in demand.
Decision theory introductory problem
- 2. DECISION MAKING UNDER RISK
- 3. Suppose an electrical goods merchant buys, for resale purposes in a market, electric irons in the range of 0 to 4. His resources permit him to buy nothing or 1 or 2 or 3 or 4 units. These are his alternative courses of action or strategies. The demand for electric irons on any day is something beyond his control and hence is a state of nature. Let us presume that the dealer does not know how many units will be bought from him by the customers. The demand could be anything from 0 to 4. The dealer can buy each unit of electric iron @ Rs.40 and sell it at Rs.45 each, his margin being Rs.5 per unit. Assume the stock on hand is valueless. Portray in a payoff table and opportunity loss table the quantum of total margin (loss), that he gets in relation to various alternative strategies and states of nature.
- 4. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 1 0–0=0 2 0–0=0 3 0–0=0 4 0–0=0
- 5. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 0–40=–40 1 0–0=0 45–40=5 2 0–0=0 45–40=5 3 0–0=0 45–40=5 4 0–0=0 45–40=5
- 6. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 0–40=–40 0–2×40=–80 0–3×40=–120 0–4×40=–160 1 0–0=0 45–40=5 45–2×40=–35 45–3×40=–75 45–4×40=–115 2 0–0=0 45–40=5 2×45–2×40=10 2×45–3×40=–30 2×45–4×40=–70 3 0–0=0 45–40=5 2×45–2×40=10 3×45–3×40=15 3×45–4×40=–25 4 0–0=0 45–40=5 2×45–2×40=10 3×45–3×40=15 4×45–4×40=20
- 7. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20
- 8. Courses of Action Probability 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40
- 9. EXPECTED MONETARY VALUE (EMV) CALCULATION
- 10. 0 1 2 3 4 P 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 𝑬𝑴𝑽 𝟎 = 𝟎 × 𝟎. 𝟎𝟒 + 𝟎 × 𝟎. 𝟎𝟔 + 𝟎 × 𝟎. 𝟐 + 𝟎 × 𝟎. 𝟑 + 𝟎 × 𝟎. 𝟒 = 𝟎
- 11. 0 1 2 3 4 P 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 𝑬𝑴𝑽 𝟎 = 𝟎 × 𝟎. 𝟎𝟒 + 𝟎 × 𝟎. 𝟎𝟔 + 𝟎 × 𝟎. 𝟐 + 𝟎 × 𝟎. 𝟑 + 𝟎 × 𝟎. 𝟒 = 𝟎 𝑬𝑴𝑽 𝟏 = −𝟒𝟎 × 𝟎. 𝟎𝟒 + 𝟓 × 𝟎. 𝟎𝟔 + 𝟓 × 𝟎. 𝟐 + 𝟓 × 𝟎. 𝟑 + 𝟓 × 𝟎. 𝟒 = 𝟑. 𝟐 𝑬𝑴𝑽 𝟐 = −𝟖𝟎 × 𝟎. 𝟎𝟒 + −𝟑𝟓 × 𝟎. 𝟎𝟔 + 𝟏𝟎 × 𝟎. 𝟐 + 𝟏𝟎 × 𝟎. 𝟑 + 𝟏𝟎 × 𝟎. 𝟒 = 𝟑. 𝟕 𝑬𝑴𝑽 𝟑 = −𝟏𝟐𝟎 × 𝟎. 𝟎𝟒 + −𝟕𝟓 × 𝟎. 𝟎𝟔 + −𝟑𝟎 × 𝟎. 𝟐 + 𝟏𝟓 × 𝟎. 𝟑 + 𝟏𝟓 × 𝟎. 𝟒 = −𝟒. 𝟖 𝑬𝑴𝑽 𝟒 = −𝟏𝟔𝟎 × 𝟎. 𝟎𝟒 + −𝟏𝟏𝟓 × 𝟎. 𝟎𝟔 + −𝟕𝟎 × 𝟎. 𝟐 + −𝟐𝟓 × 𝟎. 𝟑 + 𝟐𝟎 × 𝟎. 𝟒 = −𝟐𝟔. 𝟖
- 12. 0 1 2 3 4 P 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 EMV 0 3.2 3.7 –4.8 –26.8
- 13. 0 1 2 3 4 P 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 EMV 0 3.2 3.7 –4.8 –26.8 𝑬𝑴𝑽 𝒎𝒂𝒙 = 𝑬𝑴𝑽 𝟐 = 𝟑. 𝟕
- 14. REGRET TABLE
- 15. Payoff Table 0 1 2 3 4 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Regret/Opportunity Loss Table Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 1 5–0=5 2 10–0=10 3 15–0=15 4 20–0=20
- 16. Payoff Table 0 1 2 3 4 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Regret/Opportunity Loss Table Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 0–(–40)=40 1 5–0=5 5–5=0 2 10–0=10 10–5=5 3 15–0=15 15–5=10 4 20–0=20 20–5=15
- 17. Payoff Table 0 1 2 3 4 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Regret/Opportunity Loss Table Courses of Action 0 1 2 3 4 States of Nature 0 0–0=0 0–(–40)=40 0–(–80)=80 0–(–120)=120 0–(–160)=160 1 5–0=5 5–5=0 5–(–35)=40 5–(–75)=80 5–(–115)=120 2 10–0=10 10–5=5 10–10=0 10–(–30)=40 10–(–70)=80 3 15–0=15 15–5=10 15–10=5 15–15=0 15–(–25)=40 4 20–0=20 20–5=15 20–10=10 20–15=5 20–20=0
- 18. Regret/Opportunity Loss Table Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0
- 19. Regret/Opportunity Loss Table Courses of Action P 0 1 2 3 4 States of Nature 0 0 40 80 120 160 0.04 1 5 0 40 80 120 0.06 2 10 5 0 40 80 0.20 3 15 10 5 0 40 0.30 4 20 15 10 5 0 0.40
- 20. EXPECTED OPPORTUNITY LOSS (EOL) CALCULATION
- 21. Regret/Opportunity Loss Table Courses of Action P 0 1 2 3 4 States of Nature 0 0 40 80 120 160 0.04 1 5 0 40 80 120 0.06 2 10 5 0 40 80 0.20 3 15 10 5 0 40 0.30 4 20 15 10 5 0 0.40 𝑬𝑶𝑳 𝟎 = 𝟎 × 𝟎. 𝟎𝟒 + 𝟓 × 𝟎. 𝟎𝟔 + 𝟏𝟎 × 𝟎. 𝟐 + 𝟏𝟓 × 𝟎. 𝟑 + 𝟐𝟎 × 𝟎. 𝟒 = 𝟏𝟒. 𝟖
- 22. Regret/Opportunity Loss Table Courses of Action P 0 1 2 3 4 States of Nature 0 0 40 80 120 160 0.04 1 5 0 40 80 120 0.06 2 10 5 0 40 80 0.20 3 15 10 5 0 40 0.30 4 20 15 10 5 0 0.40 𝑬𝑶𝑳 𝟎 = 𝟎 × 𝟎. 𝟎𝟒 + 𝟓 × 𝟎. 𝟎𝟔 + 𝟏𝟎 × 𝟎. 𝟐 + 𝟏𝟓 × 𝟎. 𝟑 + 𝟐𝟎 × 𝟎. 𝟒 = 𝟏𝟒. 𝟖 𝑬𝑶𝑳 𝟏 = 𝟒𝟎 × 𝟎. 𝟎𝟒 + 𝟎 × 𝟎. 𝟎𝟔 + 𝟓 × 𝟎. 𝟐 + 𝟏𝟎 × 𝟎. 𝟑 + 𝟏𝟓 × 𝟎. 𝟒 = 𝟏𝟏. 𝟔 𝑬𝑶𝑳 𝟐 = 𝟖𝟎 × 𝟎. 𝟎𝟒 + 𝟒𝟎 × 𝟎. 𝟎𝟔 + 𝟎 × 𝟎. 𝟐 + 𝟓 × 𝟎. 𝟑 + 𝟏𝟎 × 𝟎. 𝟒 = 𝟏𝟏. 𝟏 𝑬𝑶𝑳 𝟑 = 𝟏𝟐𝟎 × 𝟎. 𝟎𝟒 + 𝟖𝟎 × 𝟎. 𝟎𝟔 + 𝟒𝟎 × 𝟎. 𝟐 + 𝟎 × 𝟎. 𝟑 + 𝟓 × 𝟎. 𝟒 = 𝟏𝟗. 𝟔 𝑬𝑶𝑳 𝟒 = 𝟏𝟔𝟎 × 𝟎. 𝟎𝟒 + 𝟏𝟐𝟎 × 𝟎. 𝟎𝟔 + 𝟖𝟎 × 𝟎. 𝟐 + 𝟒𝟎 × 𝟎. 𝟑 + 𝟎 × 𝟎. 𝟒 = 𝟒𝟏. 𝟔
- 23. Regret/Opportunity Loss Table Courses of Action P 0 1 2 3 4 States of Nature 0 0 40 80 120 160 0.04 1 5 0 40 80 120 0.06 2 10 5 0 40 80 0.20 3 15 10 5 0 40 0.30 4 20 15 10 5 0 0.40 EOL 14.8 11.6 11.1 19.6 41.6
- 24. Regret/Opportunity Loss Table Courses of Action P 0 1 2 3 4 States of Nature 0 0 40 80 120 160 0.04 1 5 0 40 80 120 0.06 2 10 5 0 40 80 0.20 3 15 10 5 0 40 0.30 4 20 15 10 5 0 0.40 EOL 14.8 11.6 11.1 19.6 41.6 𝑬𝑶𝑳 𝒎𝒊𝒏 = 𝑬𝑶𝑳 𝟐 = 𝟏𝟏. 𝟏
- 25. EXPECTED VALUE WITH PERFECT INFORMATION EV with PI
- 26. Payoff Matrix Courses of Action P 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 = 𝚺 𝑴𝒂𝒙 𝑬𝑴𝑽 𝒇𝒐𝒓 𝒆𝒂𝒄𝒉 𝑺𝒕𝒂𝒕𝒆 𝒐𝒇 𝑵𝒂𝒕𝒖𝒓𝒆 × 𝑷
- 27. Payoff Matrix Courses of Action P 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 = 𝚺 𝑴𝒂𝒙 𝑬𝑴𝑽 𝒇𝒐𝒓 𝒆𝒂𝒄𝒉 𝑺𝒕𝒂𝒕𝒆 𝒐𝒇 𝑵𝒂𝒕𝒖𝒓𝒆 × 𝑷
- 28. Payoff Matrix Courses of Action P 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 0.04 1 0 5 –35 –75 –115 0.06 2 0 5 10 –30 –70 0.20 3 0 5 10 15 –25 0.30 4 0 5 10 15 20 0.40 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 = 𝟎 × 𝟎. 𝟎𝟒 + 𝟓 × 𝟎. 𝟎𝟔 + 𝟏𝟎 × 𝟎. 𝟐 + 𝟏𝟓 × 𝟎. 𝟑 + 𝟐𝟎 × 𝟎. 𝟒 ∴ 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 = 𝟏𝟒. 𝟖
- 29. EXPECTED VALUE OF PERFECT INFORMATION EVPI
- 30. 𝑬𝑽𝑷𝑰 = 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 − 𝑬𝑴𝑽 𝒎𝒂𝒙 𝒐𝒓 𝑬𝑽𝑷𝑰 = 𝟏𝟒. 𝟖 − 𝟑. 𝟕 𝒐𝒓 𝑬𝑽𝑷𝑰 = 𝟏𝟏. 𝟏
- 31. 𝑬𝑽𝑷𝑰 = 𝑬𝑽 𝒘𝒊𝒕𝒉 𝑷𝑰 − 𝑬𝑴𝑽 𝒎𝒂𝒙 𝒐𝒓 𝑬𝑽𝑷𝑰 = 𝟏𝟒. 𝟖 − 𝟑. 𝟕 𝒐𝒓 𝑬𝑽𝑷𝑰 = 𝟏𝟏. 𝟏 𝑨𝒍𝒕𝒆𝒓𝒏𝒂𝒕𝒆𝒍𝒚, 𝑬𝑽𝑷𝑰 = 𝑬𝑶𝑳 𝒎𝒊𝒏 = 𝑬𝑶𝑳 𝟐 = 𝟏𝟏. 𝟏
- 33. DECISION CRITERIA UNDER CONDITION OF UNCERTAINTY • Maximin. • Maximax. • Minimax Regret. • Hurwicz Criterion. • Baye’s/Lapalce’s Criterion.
- 34. CRITERION OF PESSIMISM (MAXIMIN) • Also called ‘Waldian Criterion.’ • Determine the lowest outcome for each alternative. • Choose the alternative associated with the best of these.
- 35. CRITERION OF OPTIMISM (MAXIMAX) • Suggested by Leonid Hurwicz. • Determine the best outcome for each alternative. • Select the alternative associated with the best of these.
- 36. MINIMAX REGRET CRITERION • Attributed to Leonard Savage. • For each state, identify the most attractive alternative. • Place a zero in those cells. • Compute opportunity loss for other alternatives. • Identify the maximum opportunity loss for each alternative. • Select the alternative associated with the lowest of these.
- 37. CRITERION OF REALISM (HURWICZ CRITERION) • A compromise between maximax and maximin criteria. • A coefficient of optimism α (0≤α≤1) is selected. • When α is close to 1, the decision-maker is optimistic about the future. • When α is close to 0, the decision-maker is pessimistic about the future.
- 38. HURWICZ CRITERION • Select the strategy which maximises:
- 39. LAPLACE CRITERION • Assign equal probabilities to each state. • Compute the expected value for each alternative. • Select the alternative with the highest alternative.
- 40. CRITERION OF PESSIMISM (MAXIMIN)
- 41. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20
- 42. Payoff Matrix: Maximin Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 𝑴𝒂𝒙𝒊𝒎𝒊𝒏 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒊𝒏𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 43. Payoff Matrix: Maximin Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Minima 0 –40 –80 –120 –160 𝑴𝒂𝒙𝒊𝒎𝒊𝒏 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒊𝒏𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 44. Payoff Matrix: Maximin Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Minima 0 –40 –80 –120 –160 Maximum of the column minima=0 𝑴𝒂𝒙𝒊𝒎𝒊𝒏 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒊𝒏𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 45. Payoff Matrix: Maximin Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Minima 0 –40 –80 –120 –160 Maximum of the column minima=0 𝑴𝒂𝒙𝒊𝒎𝒊𝒏 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒊𝒏𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓 ∴ 𝒕𝒉𝒆 𝒃𝒆𝒔𝒕 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒂𝒄𝒄𝒐𝒓𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒊𝒏 𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 = 𝟎
- 46. CRITERION OF OPTIMISM (MAXIMAX)
- 47. Payoff Matrix Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20
- 48. Payoff Matrix: Maximax Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 𝑴𝒂𝒙𝒊𝒎𝒂𝒙 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 49. Payoff Matrix: Maximax Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Maxima 0 5 10 15 20 𝑴𝒂𝒙𝒊𝒎𝒂𝒙 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 50. Payoff Matrix: Maximax Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Maxima 0 5 10 15 20 Maximum of the column maxima=20 𝑴𝒂𝒙𝒊𝒎𝒂𝒙 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 51. Payoff Matrix: Maximax Criterion Courses of Action 0 1 2 3 4 States of Nature 0 0 –40 –80 –120 –160 1 0 5 –35 –75 –115 2 0 5 10 –30 –70 3 0 5 10 15 –25 4 0 5 10 15 20 Column Maxima 0 5 10 15 20 Maximum of the column maxima=20 𝑴𝒂𝒙𝒊𝒎𝒂𝒙 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒑𝒂𝒚𝒐𝒇𝒇𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒑𝒂𝒚𝒐𝒇𝒇 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓 ∴ 𝒕𝒉𝒆 𝒃𝒆𝒔𝒕 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒂𝒄𝒄𝒐𝒓𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒂𝒙 𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 = 𝟒
- 53. Regret/Opportunity Loss Table Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0
- 54. Regret Table (Minimax Regret Criterion) Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0 𝑴𝒊𝒏𝒊𝒎𝒂𝒙 𝑹𝒆𝒈𝒓𝒆𝒕 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 (𝒊𝒏 𝒕𝒉𝒆 𝒓𝒆𝒈𝒓𝒆𝒕 𝒕𝒂𝒃𝒍𝒆) ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒓𝒆𝒈𝒓𝒆𝒕𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 55. Regret Table (Minimax Regret Criterion) Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0 𝑴𝒊𝒏𝒊𝒎𝒂𝒙 𝑹𝒆𝒈𝒓𝒆𝒕 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 (𝒊𝒏 𝒕𝒉𝒆 𝒓𝒆𝒈𝒓𝒆𝒕 𝒕𝒂𝒃𝒍𝒆) ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒓𝒆𝒈𝒓𝒆𝒕𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 56. Regret Table (Minimax Regret Criterion) Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0 Column maxima 20 40 80 120 160 𝑴𝒊𝒏𝒊𝒎𝒂𝒙 𝑹𝒆𝒈𝒓𝒆𝒕 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 (𝒊𝒏 𝒕𝒉𝒆 𝒓𝒆𝒈𝒓𝒆𝒕 𝒕𝒂𝒃𝒍𝒆) ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒓𝒆𝒈𝒓𝒆𝒕𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 57. Regret Table (Minimax Regret Criterion) Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0 Column maxima 20 40 80 120 160 Minimum of the column maxima=20 𝑴𝒊𝒏𝒊𝒎𝒂𝒙 𝑹𝒆𝒈𝒓𝒆𝒕 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 (𝒊𝒏 𝒕𝒉𝒆 𝒓𝒆𝒈𝒓𝒆𝒕 𝒕𝒂𝒃𝒍𝒆) ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒓𝒆𝒈𝒓𝒆𝒕𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓
- 58. Regret Table (Minimax Regret Criterion) Courses of Action 0 1 2 3 4 States of Nature 0 0 40 80 120 160 1 5 0 40 80 120 2 10 5 0 40 80 3 15 10 5 0 40 4 20 15 10 5 0 Column maxima 20 40 80 120 160 Minimum of the column maxima=20 𝑴𝒊𝒏𝒊𝒎𝒂𝒙 𝑹𝒆𝒈𝒓𝒆𝒕 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏: ≫ 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒐𝒍𝒖𝒎𝒏 𝒎𝒂𝒙𝒊𝒎𝒂 (𝒊𝒏 𝒕𝒉𝒆 𝒓𝒆𝒈𝒓𝒆𝒕 𝒕𝒂𝒃𝒍𝒆) ≫ 𝒊. 𝒆. , 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒄𝒐𝒍𝒖𝒎𝒏 ≫ 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆 𝒓𝒆𝒈𝒓𝒆𝒕𝒔 ≫ 𝑻𝒉𝒆 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒕𝒐 𝒕𝒉𝒊𝒔 𝒓𝒆𝒈𝒓𝒆𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓 ∴ 𝒕𝒉𝒆 𝒃𝒆𝒔𝒕 𝒄𝒐𝒖𝒓𝒔𝒆 𝒐𝒇 𝒂𝒄𝒕𝒊𝒐𝒏 = 𝟎