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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17
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6answers
631 views

Experiments contradicting the expected utility model

This is a question I asked on the cognitive science beta which never got any answer there. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?)...
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3answers
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Current knowledge about the empirics of consumer theory

I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.). Can anyone ...
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Intuition behind risk premium

In Lecture 20 of MIT's Microeconomics course, a situation is proposed where a 50/50 bet will either result in losing \$100 or gaining \$125 with a starting wealth of \$100. It is stated that a person ...
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2answers
788 views

Can the Machina Paradox be solved by expanding the choice set?

In another question, the Machina paradox is mentioned as a possible counterexample to the expected utility model: Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-...
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4answers
622 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. ...
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3answers
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Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
9
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1answer
230 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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1answer
3k views

Continuity Axiom in Expected Utility Theory

Take the following definition of continuity. The preference relation $\succsim$ over the space of lotteries $\mathcal L$ is continuous if for any $L,L',L''\in\mathcal L$, the sets $$S_1=\{\...
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1answer
603 views

Preference over lotteries without independence axiom

Suppose a set of $N$ outcomes can be ranked in the following order: $1\succ 2\succsim\cdots\succsim N$. Further, suppose a decision maker has preference over lotteries over these outcomes. Assume the ...
8
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2answers
407 views

Will high computing power substitute the certainty-equivalence assumption?

Bloom in a recent JEP paper considers that "the increase in computing power has made it possible to include uncertainty shocks directly in a wide range of models, allowing economists to abandon ...
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1answer
441 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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4answers
189 views

What are different ways of specifying utility and decision making?

This question is related to this question about the Machina paradox and about the expected utility model. In this question, I'd like to know a little more about various or even competing ways of ...
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2answers
388 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
531 views

Anscombe-Aumann Acts and Lotteries

Notation: Throughout I will let $\Delta X$ denote the set of probability distributions over the set $X$. I have been studying expected utility theory, and especially Savage Acts and Anscombe-Aumann ...
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3answers
612 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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1answer
292 views

Time costs and the St. Petersburg paradox

In the St. Petersburg paradox, we end up with the problem that a rational agent should be willing to play the game for any wager, if we look at expected income or utility of expected income. The ...
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1answer
75 views

Meaning of $dF(z)$ in expected utility framework

Background: from a Microeconomics course, $F$ is a cdf. In other words, if $F$ has a density function $f$, then $$F(z)={\int_{-\infty}^z f(x) dx} $$ Write the Bernoulli utility function $u:...
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2answers
126 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. ...
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1answer
268 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 ...
6
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1answer
358 views

Does vNM rationality depend on the good chosen?

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
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1answer
118 views

What is the consensus (if any) on Peters “The ergodicity problem in economics” (2019)?

Peters (2019) made a splash criticizing the theory of expected utility on the grounds that it implicitly assumes ergodicity where this is unwarranted. He stated this applies widely in economics, to ...
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1answer
359 views

How does expected utility theory treat losses?

I've been reading about prospect theory lately and have read often that prospect theory predicts people will be risk averse in gains and risk seeking in losses. This statement is typically ...
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3answers
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Question about the Ellsberg Paradox in Expected Utility Theory

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
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0answers
301 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 ...
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2answers
2k views

Risk Premium in the Expected Utility Theory

Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$ Eu(w+x) = u(w+E(x)-R). $$ The classical derivation ...
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1answer
76 views

Who is the first one to equate “rational” with “complete and transitive preference”?

MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first? vNM said ...
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1answer
109 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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2answers
487 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 $P'$ $\implies$ $aP + (1-a)P''$ preferred to ...
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2answers
396 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. ...
4
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1answer
285 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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3answers
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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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3answers
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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
110 views

Expected utility theory (Lottery notation)

A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences $$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ ...
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1answer
331 views

Why is the risk premium always positive for risk averse individuals?

I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.
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4answers
172 views

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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2answers
270 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
2k views

Reverse auction formula

I am studing a little bit of auction theory. I found the optimal bid value in the Milgrom paper for the first price auction that is $$ P=v \frac{n-1}{n} $$ where $P$ is the optimal bid, $v$ is the ...
3
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1answer
104 views

Why utility rather than expected utility in Cochrane's “Asset Pricing”?

Cochrane "Asset Pricing" Chapter 1 p. 6 says We model investors by a utility function defined over current and future values of consumption, $$ U(c_t,c_{t+1}) = u(c_t) + \beta \mathbb{E_t}[...
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1answer
99 views

Should the “value function” be “utility function” in prospect theory?

I have a background in mathematics rather than economics, and currently reading Choices, Values, and Frames[1]. The paper defines a "hypothetical value function" (the s-shape that is concave ...
3
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1answer
6k 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 ...
3
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1answer
117 views

Diminishing mariginal utility and risk preferences

Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it ...
3
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3answers
64 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 ...
3
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1answer
92 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
88 views

Intertemporal choice with possibility of death

Here is the setup: Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by: $$...
3
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1answer
177 views

What's is the purpose of “conditional preferences” as specified in Savage's framework?

In this paper, "Savages’ Subjective Expected Utility Model" by Edi Karni, he gives a definition of "conditional preferences." See here: What situation is this supposed to capture? It seems like it ...
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0answers
52 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
240 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 $...
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1answer
320 views

Decision Theory Question: Existence and uniqueness of the certainty equivalent of p

Let $X = (x_*,x^*)$ be an interval in the real line and denote by $\Delta(X)$ the set of simple probability distributions on $X$. Consider a preference relation $\succcurlyeq$ on $\Delta(X)$ that ...
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1answer
281 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
279 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 ...