Bob has a utility function over lotteries with equally likely monetary payoffs and . This function is an example of

Question

Bob has a utility function  over lotteries with equally likely monetary payoffs  and . This function is an example of

BlackTom AI · Accepted Answer

Because Bob's utility for the lottery is written as the probability-weighted average of payoffs' utilities, it matches the expected-utility form.

1. Relevant knowledge points and concepts
- A lottery assigns outcomes x, y with probabilities p, 1−p. 
- The expected-utility (von Neumann–Morgenstern) representation says the utility of a lottery is the sum of outcome utilities weighted by their probabilities: U(L) = Σ p_i u(x_i). 
- Expected value would weight monetary amounts themselves, not utilities: EV = Σ p_i x_i. 
- Prospect theory alters weights (probability weighting, reference dependence), so it is not simply the linear probability-weighted utility.

2. Complete reasoning process step by step
- Suppose the lottery L gives monetary payoff x with probability 1/2 and y with probability 1/2.
- If Bob’s utility over the lottery is u(L) = (1/2) u(x) + (1/2) u(y), this is exactly the probability-weighted sum of utilities for each outcome.

3. Calculations and intermediate steps
- Write probabilities p1 = 1/2, p2 = 1/2.
- Expected utility: U(L) = p1 u(x) + p2 u(y) = (1/2) u(x) + (1/2) u(y).
- No further simplification is necessary; the form is linear in probabilities.

4. Why the correct answer is correct
- The form U(L) = Σ p_i u(x_i) is the defining property of an expected-utility function under von Neumann–Morgenstern axioms. Because Bob’s utility for the lottery equals the weighted sum of the utilities of monetary outcomes with their probabilities, it is an expected-utility representation.

5. Why the other options are incorrect
- Expected value would be (1/2)x + (1/2)y (average monetary payoff), not (1/2)u(x) + (1/2)u(y). 
- Prospect theory typically uses probability weighting and reference-dependent value functions, so it does not reduce to a simple linear probability-weighted utility unless special parameters force it to; the standard label is not prospect theory.
- “None of the above” is incorrect because the expression exactly matches expected utility.

6. Conclusion
- Therefore the function is an example of expected utility, which matches the provided answer.

Bob has a utility function over lotteries with equally likely monetary payoffs and . This function is an example of单项选择题

类似问题

Identify the truthfulness of the following statements: In economics, a lottery describes any choice for which the outcome is uncertain. The independence axiom is a requirement of rationality in the presence of uncertainty.

Alice maximizes expected utility with an index u(x)=−2−0.01x. Then Alice will reject a gamble that loses $100 with probability 1/2 and gains one billion dollars with probability 1/2. This observation illustrates

Alice maximizes expected utility with an index u(x)=−2−0.01x. What is true about Alice's behavior?

Bob has a utility function U(x,y)=−2−x−2−y over lotteries with equally likely monetary payoffs x and y. This function is an example of

The implementation and loading phase of the Database Life Cycle (DBLC) involves _____.

Which of the following parameters is used to determine the concentration of protein in a spectrophotometer?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单