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Tradeoff Method for EU and NonEU Prospect Theory

Explore the tradeoff method for both Expected Utility (EU) and nonEU Prospect Theory, analyzing misperceived probabilities and utility graphs under different scenarios. The method involves comparing utility values such as U(8000) and U(1000) to make informed decisions. Learn how to draw utility graphs, normalize utility values, and draw conclusions based on the data. Understand the process step by step and apply it to various situations.

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Tradeoff Method for EU and NonEU Prospect Theory

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  1. x1 200,000 ½ ½ ~ ½ ½ ½ ½ _ _ 1/2 1/2 (U(8000)-U(1000)) (U(8000)-U(1000)) ½ ~ ½ 8000 8000 1000 1000 1/2 1/2 ~ = ½ ½ . . . ½ ½ = 1 Tradeoff (TO) method for EU ½(U(x1)-U(x0)) = ½(U(8000) - U(1000)) ½U(1000) + ½U(x1) = ½U(8000) + ½U(x0) EU 8000 1000 _ 1/2 U(x1)-U(x0)= (U(8000)-U(1000))  1/2 12,000 10,000 (=x0) = U(x2)-U(x1)= x1 x2 . . . U(x4)-U(x3)= x3 x4

  2. U 3/4 2/4 1/4 x3 € 2 Let's draw a graph of U. Consequently: U(xj) = j/4. Normalize: U(x0) = 0; U(x4) = 1. 1 0 x1 x2 x0 x4

  3. x1 200,000 ½ d1 d1 d1 ~ ½ ? ! ½ ½ _ _ 1/2 1/2 (U(8000)-U(1000)) (U(8000)-U(1000)) ½ ~ ½ 8000 8000 1000 1000 d2 d2 d2 1/2 1/2 ~ = ! ? ½ ½ . . . ½ ½ = ! ? 3 Tradeoff (TO) method for nonEU Prospect theory: misperceived probs (even unknown probs) EU ½ 8000 1000 _ 1/2 U(x1)-U(x0)= (U(8000)-U(1000))  1/2 12,000 10,000 ½ (=x0) = U(x2)-U(x1)= x1 x2 . . . U(x4)-U(x3)= x3 x4

  4. U 1 3/4 2/4 0 1/4 x1 x2 x0 x4 x3 € 4 Conclusion about graph of U: Is also valid utility graph under nonEU/prospect theory.

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