# Questions tagged [expected-utility]

The expected utility theory deals with the analysis of choices among risky projects with multiple possible outcomes.

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### Lucas 1972 Neutrality of Money Proof of derivation

Lucas (1972) Neutrality of Money section 3 has following set up. $U(c,n)$ is Utility function of consumption and labor (or producing labor output). $U_c (c,n) >0$ and $U_n (c,n)<0$. Further, the ...
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### how to reach Continuous Expected Utility (EU)?

Consider EU on monetary outcomes. Say we have a utility function $u:\mathbb R\to\mathbb R$ The common axioms of EU are continuity, independence and weak order. These axioms do not imply that the ...
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### How could define the certainty equivalent in a Bayesian Persuasion model?

For once again I will start describing the Kamenica and Gentzkow Bayesian persuasion model. Suppose that $\Theta$ is a finite set of states and $\theta$ is the element of the state set. To simplify ...
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### Non-nullity assumption in vNM theorem of cardinal utility

The vNM theorem suggests that weak-ordering, continuity, and independence is equivalent to the existence of expected utility, unique up to an affine transformation. In Savage's axioms of expected ...
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### A Measure Theory\Probability Question Regarding Model Setting of Ambiguity (Schmeidler (1984, 1989))

In David Schmeidler (1984), "Subjective Probability and Expected Utility without Additivity", "2. Axioms and Background", there is a setting: Let $X$ be a set and let $Y$ be the ...
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### Independence Axiom and Expected Utility Theorem Proof

In my micro class we covered the proof of the existence of a Von Neumann–Morgenstern utility representation of preferences $\succeq$ over a set of lotteries $\Delta(Z)$ - where $Z$ is some finite ...
1 vote
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### Can we use the utility of discounted flows to do asset pricing?

Is it possible to do asset pricing by using the expected utility of the present value of all future discounted cash flows ? I aim to use this utility function to define an optimal portfolio, but I ...
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### Degrees of Risk aversion and Expected utility [closed]

There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
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### Comparing agent decision-making under risk-neutrality and risk-Aversion

I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows: There is a technology (for example, a vaccine) which reduces the ...
1 vote
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### How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
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### How special is the "expected value" operator in Von Neumann–Morgenstern utility theorem?

The Von Neumann–Morgenstern utility theorem states that For any VNM-rational agent (i.e. satisfying axioms 1–4), there exists a function $u$ which assigns to each outcome $A$ a real number $u(A)$ ...
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### Decision theory: elicitation method

I'm stuck with the following question: Let's say that C1, C2 and C3 represent the certainty equivalents and (x,p,y) the prospects. C1 ~ (x, p, 0) C2 ~ (x, p, C1) C3 ~ (C1, p, 0) What is C3 such that ...
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### Bernoulli, Ergodicity, Ole Peters

You may or may not be aware that there's a Simple English Wikipedia. It's very helpful for those of us who know English, but are unable to parse complex sentences (for whatever reason). I'm very ...
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### What is the relation between Blackwell's order and Stochastic Dominance order?

In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
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### Ratio of two Jensen inequality

I have these pair of numbers $(a, b) = (\frac{4}{9}, \frac{1}{9})$ and $(c, d) = (\frac{1}{2}, \frac{1}{6})$. (Number mean nothing, just for illustration and simplification) Note that - (a, b) are ...
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### What does the empirical literature tell us about the relative merits of alternative functional forms describing the marginal utility of income?

Among the various functional forms that have been used on model the marginal utility of income in, e.g., in making decisions under uncertainty, and perhaps intertemporal choice as well, is the ...
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### About Theorem 1.1 (the Expected-Utility Maximization Theorem) in Game Theory: Analysis of Conflict by Roger Myerson

I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his proof of Theorem 1.1, the Expected-Utility Maximization Theorem. The Theorem goes ...
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### What is the difference between utility, payoff and expected utility, or are the terms interchangeable?

I've started teaching myself game theory recently, but so far I haven't come across anything clarifying these terms . This is my understanding of the terms based on what I know: Payoff = Utility. ...
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### Proof of the Lucas' Cost of Business Cycles

I am trying to derive the parameter used by Lucas to measure the cost of business cycles, namely: derived in the paper "Macroeconomic Priorities". I already searched in several papers but I ...
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### Expected utility maximization question

If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ...
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### Deriving the CAPM: going from utility of consumption to utility of asset returns

Some textbook presentations of the capital asset pricing model (CAPM) take returns on stocks as a primitive and proceed as if agents derive utility from asset returns. Assuming a concave utility ...
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### Expected Utility

I really don't know how to interpret the graph. Can someone help me? I thought of doing 0.6253+0.3751 to find the expected value of the lottery but where is the sure bet?
1 vote
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### Existence of best and worst lotteries with finite outcome set and IIA

In the context of expected utility theory, I want to prove that if the set of outcomes is finite and an agent has a rational preference relation over the set of lotteries, and if that preference ...
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### Expected revenue maximizing auction & ex-post efficiency

Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?
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### Convergence of various forms of Prospect Theory?

I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience. My problem is the following: I want to analyse the effects ...
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### Von Neumann-Morgenstern Utility Theory Question

There's a question in my ECON notes that I don't understand, any help would be greatly appreciated. Here are the definitions used about VNM Utility Theory. The question is posted after the definitions....
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### Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU? To my knowledge, most utility functions under risk and ...
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### Utility of both players in St. Petersbourg paradox - behavioural economics

Im reading a paper by Karl Menger [1] about the St. Peterbourg paradox : In the theory of probability, the "Petersburg Game" designates the follow- ing gamei between two persons, A and B. ...
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### What is the intuition behind Expected Utility Theorem?

I am referring to the definition in Proposition 6.B.3 on Page 176 of Mas Colell. I follow the formal proof and the application of the Independence axiom at various steps (mathematical application of ...
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### certainty equivalent and lotteries [closed]

suppose an agent has $u(z)=-e^{-bz}$ where $b>0$ as her Bernoulli utility function and faces two gambles: G1: win 1000 dollars with probability $\frac{1}{2}$ and zero with probability $\frac{1}{2}$ ...
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