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Questions tagged [expected-utility]

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Can I recreate an experiment on Allais paradox using student grades as payoffs?

For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money. Is this reformulation of the Allais ...
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0answers
27 views

Does Pascal's Wager fail archimedean property?

I assume most people have heard of Pascal's Wager, in case you have not: https://en.wikipedia.org/wiki/Pascal%27s_Wager By the Stanford encyclopedia of philosphy: "We have a decision under risk,...
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1answer
42 views

Existence of 'best' and 'worst' lottery

How can 'the best and worst lotteries exist when the set of outcome is finite and the rational preference relation satisfies independence axiom' be proven?
2
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1answer
80 views

Proof of Expected utility theorem with three outcomes

I am trying to prove the expected utility theorem with three outcomes. The expected utility with $n$ outcomes is rather cumbersome and long in the economics textbook Mas-Colell. But I was hoping that ...
0
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1answer
31 views

Theories that complement/contradict prospect theory?

Kahneman and Tversky's prospect theory, which they developed to contradict expected utility theory, is obviously an interesting result. But, after their experiments has anyone tried to completement ...
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Two formulations of the continuity axiom in Expected Utility Theory

MWG state the continuity axiom as follows: C1. $\succsim$ is continuous if for all $L,L',L''$, the two sets below are both closed: \begin{align} S&=\{\alpha\in[0,1]:\alpha L+(1-\alpha)L''\...
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Why do we say the vNM Expected Utility Function can only deal with objective probabilities?

I'm trying to learn about decision theory, and they've just introduced Anscombe Aumann Expected Utility. The reason they needed this new layer, they claim, is that we can't understand the decision-...
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30 views

Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
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1answer
15 views

advanced mathematical treatement of revealed preference and utility theory?

I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel. What would be suggestions for this? Specifically I'm interested in conditions ...
2
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1answer
44 views

Construct utility function for a risk-averse agent

I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
5
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2answers
160 views

Does the Prospect Theory value curve change according to reference wealth size?

After reading "Thinking Fast and Slow" and half a day of internet search on this topic I resort now to asking this question here. Prospect Theory seems to only attribute value to changes in wealth. ...
2
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1answer
38 views

Can number of children in rich country is small due to this simple economic factor?

In rich countries, people are expensive. Even taxi driver in Singapore earns $6k per month. Now, the "market" tend to correct it self. If something is expensive, and it's marginal productivity is ...
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Lotteries and expected utility

Suppose we have the following four lotteries: $L_{1}=[(1,\$1)]$ $L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$ $L_{3}=[(0.9,\$0),(0.1,\$5)]$ $L_{4}=[(0.89,\$0),(0.11,\$1)]$ If our agent says that he ...
3
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3answers
51 views

Expected values vs uncertainty

Most models I have seen use expected values. Why is this a better economic model than uncertainty and economic agents thus having to make 'best guesses', with the result of 'animal spirits' playing a ...
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0answers
32 views

Literature on Recursive Preferences and Time-Additive Expected Utility

In Chapter 20 of the book Economic Dynamics in Discrete Time, named "Recursive Utility", the author asserts that the Time-Additive Expected Utility Model (TAEU) has some shortcomings when applied to ...
2
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1answer
113 views

Is there a dutch book argument for the “independence of irrelevant alternatives” axiom?

There is a dutch book argument to show that nontransitive preferences are in a sense "unreasonable", which justifies why we pose the axiom of transitivity in the definition of "rational preferences", ...
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45 views

Analyse empirical data with Prospect Theory and Expected Utility Theory

I would like to compare the preference function of Prospect Theory against classical Expected Utility Theory, using empirical data representing gains and losses. What utility should I choose for ...
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2answers
469 views

How to calculate Shapley Value with uncertainty?

So I'm trying to estimate a Shapley value in a game with uncertain payoffs. Specifically, imagine a game where the payoff function as as follows ...
3
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2answers
107 views

What are some non-von-Neumann-Morgenstern preferences used in economics?

Von-Neumann Morgenstern preferences are preferences over lotteries that can be represented as the expectation of a "deterministic" utility function over outcomes. "non-von-Neumann-Morgenstern" ...
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1answer
112 views

Modelling Bounded Utility Functions

I'm trying to work out how to model a utility function that is bounded below some level. More precisely, given a specified limit $L$, I want to work out how to ensure that the utility of any outcome $...
3
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1answer
37 views

Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$. Are there intuitive interpretations of the numerical values of these ...
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1answer
281 views

vNM Expected Utility Theorem Proof

I have been asked by my professor for Decisions Theory to refer to David M. Kreps' Notes on Theory of Choice for the proof of the vNM theorem of expected utility. Before the proof of the theorem ...
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1answer
122 views

Maximal Allais paradox

The Allais paradox, is an experiment set up as follows, where you are free to chose between gambles $A$ and $B$: (the table on wikipedia is much more readable if you prefer) Experiment 1 ...
2
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1answer
163 views

Prove relation between expected utility and utility of the mean

Assume $U(x)$ is a concave, monotonically increasing function. If we know that $$U\left[E(p)\right] > U\left[E(q)\right]$$ where $p$ and $q$ are probability distributions, how can we prove that ...
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1answer
43 views

How do economists model VNM-rationality violation?

This question concerns the need to generalise utility maximisation, the fact that it's a special case of a general problem familiar to physicists, and the question of whether economists have affected ...
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3answers
896 views

Utility of expected income or expected utility of income?

Currently I am reviewing microeconomic material related to utility maximization due to an upcoming examination. One old exam question asks me the following for which I am not sure whether to use the ...
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1answer
2k views

von-Neumann-Morgenstern v. Bernoulli Utility Function

A great deal of time is spent distinguishing the big $U$ (von-Neumann-Morgenstern)v. small $u$ (Bernoulli Utility Function). The v.NM function maps from the space of lotteries to real number as it ...
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0answers
155 views

How a utility function which is both DARA and CRRA can be explained?

I'm studying risk aversion and I cannot make a intuitive explain about the utility function which is DARA and CRRA. for instance, let's say, $\ln W$, where $W$ stands for one's wealth. by the ...
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1answer
111 views

How can the VNM completeness axiom be derived from the transitivity and continuity axioms?

My teacher mentioned off-hand that the first Von Neumann Morgenstern axiom of completeness is not actually necessary to prove the Expected Utility Property, and that the axiom of completeness is in ...
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1answer
76 views

Additive multiattribute nonlinear utility functions

I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form: $u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \...
3
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0answers
447 views

Certainty Equivalents and Risk Premiums in Expected Utility Theory for Asymmetric Distributions

I want to calculte risk-premiums in order to assess how much risk-averse customers would be willing to pay for an insurance against an uncertain loss modeled by a random variable $X$. How would a risk-...
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1answer
2k views

Certainty equivalent and risk aversion parameter given utility function

I know this is rather easy but I do not have any example or material to really work from that I could find online. Consider an agent with a utility index over wealth given by $$v(w) = \frac{w^{1 - \...
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3answers
390 views

An agent's expected utility depends only on mean and variance

Consider an agent with the expected utility function $U(L) = \sum_{s=1}^{S}\pi_s U(Y_s)$ over the lottery $L = (Y_s, \pi_s)$ where $\pi_s$ is the probability of state $s$, $Y_s$ are state $s$ payoffs, ...
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147 views

On the uniqueness of utility functions for both risk and time

I have a question regarding the uniqueness of preference functionals under risky and dynamic settings. Two well known models to represent preferences for both settings are the Expected Utility Model ...
6
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1answer
153 views

Why is it possible to calibrate your subjective probabilities?

Humans tend to be overconfident in their predictions; when most people say that there's a 95% chance that something will happen, they're usually wrong far more than 5% of the time. Whereas what ought ...
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0answers
26 views

Is maximal utility conditional on information linear in convex combinations of priors?

This is related to a Mathematica question here - https://math.stackexchange.com/q/1952779/374929 Is a (maximal expected utility) function of the form $U(\mu, X) \equiv \int_\Theta \int_\mathcal{X} \...
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2answers
101 views

Have there been attempts to measure the value of specific taught skills?

I'm aware there is a body of research concerned with measuring the returns to schooling in general, and there are theoretical pronouncements about what the most valuable things to learn at school are. ...
3
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1answer
198 views

Microeconomics - Expected Utility Theory - Piecewise utility index, certainty equivalence, etc.

I am solving old problems from various qualifiers from different universities to prepare myself for an upcoming test. I came across this and wanted to ask if anyone can confirm my answers? My ...
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313 views

Why should the statistical value of life exist?

In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts. So economists have ...
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1answer
180 views

Transforming expected utility functions

I am using the following theorem: To better understand how I can transform expected utility functions. An example with which to work: I want to show that the preferences represented here satisfy ...
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2answers
474 views

How to have same utility function for two persons?

I have a question regarding utility functions: Utility can be defined as follows: $U=1+e^{\frac{x}{RT}}$ U:Utility x: What we want to find the utility for (Certain equivalent) RT: Risk tolerance ...
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2answers
313 views

Does the Independence Axiom Require Statistical Independence?

First: Given this definition of the Independence Axiom, If for all $P$, $P'$, $P''$ in the set of lotteries over outcome space $X$, when: $P$ preferred to $P'$ $\implies$ $aP + (1-a)P''$ ...
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259 views

LEN-Model equivalency

Starting position is a principal-agent-model with incomplete information (moral hazard) and the following properties: Agent utility: $u(z)=-e^{(-r_az)}$ Principal utility: $B(z)=-e^{(-r_pz)}$ Effort ...
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39 views

Utility theory or decision theory based on partial semiorders?

Roubens, Vincke & Pirlot have summarized and extended representation theorems for partial semiorders in the 80s and 90s. See e.g. Roubens, M. & Vincke, P.: Preference Modelling. Springer, 1985....
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1answer
129 views

Conceptual explanation/prediction of utility function. Extraction of utility function from Big Data

It seems to me, that utility function usually is just a set of facts. Is there a framework or model for utility function that can explain or predict utility function. I. e. if user has value for item ...
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335 views

Envelope Paradox

There are two envelopes. One contains $x$ money and the other contains $2x$ amount of money. The exact amount "$x$" is unknown to me, but I know the above. I pick one envelope and I open it. I see $y$ ...
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1answer
88 views

A Deceptive Raffle

Suppose we have a hungry fox. He has a gigantic bunch of spoiled carrots that he cannot eat (and wouldn't eat if they were fresh anyway), but he knows the local bunnies in the neighboring area love ...
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1answer
651 views

How to calculate expected revenue in reverse auctions (procurement)

I'm trying to find the correct formula to calculate de expected revenue of a reverse auction, properly, a second-price sealed-bid procurement auction to identify the lowest cost supplier. Prices are ...
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45 views

How does supply and demand determine price for the following scenario?

Two individuals are stranded on an island. Bob and Jill. By themselves they can produce: Bob: 5 fish & 5 coconuts Jill: 5 fish & 5 coconuts If they specialize and trade, they can produce: ...
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1answer
196 views

Proving the De Finetti Theorem

Let us have a finite state space, $\Omega = {\omega_1,\cdots,\omega_s}$, where $2 \leq s < \infty$. Define a bet as a function $x:\Omega \rightarrow X$, where $X \subseteq \mathbb{R}^s$ is the set ...