12
votes
Accepted
Continuity Axiom in Expected Utility Theory
It is.
Prior to continuity, which is a property of the preference relation, the preference relation $\succsim$ itself has been defined to be a binary relation that is characterized by transitivity, ...
- 32.9k
11
votes
What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?
Well there is no opinion poll among economists on specifically this problem, but what can be judged from reaction of economists the consensus is that the Ole Peters paper is misguided and irrelevant ...
- 50.1k
10
votes
An agent's expected utility depends only on mean and variance
In order to understand this problem, I will work through the generic case. Say that a user had generalized quadratic (Bernoulli) utility, similar to your problem:
$$u(x) = \beta x^2 + \gamma x$$
and ...
- 6,516
9
votes
Accepted
Risk Premium in the Expected Utility Theory
Is there any (economic) rational for the first-order expansion of the RHS? And for its different neighborhood evaluation?
As for your first question:
This is a purely mathematical tactic in order to ...
- 32.9k
9
votes
Accepted
Intuition behind risk premium
The name for the amount $56.25 is certainty equivalent.
The expected utility for the individual from taking the bet is calculated as follows:
$$E[U]=\frac12U(100+125)+\frac12U(100-100)=75$$
Suppose ...
- 15.1k
9
votes
Accepted
An agent's expected utility depends only on mean and variance
\begin{eqnarray*} \displaystyle U(L) & = &\sum_{s=1}^{S}\pi_s U(Y_s) = \sum_{s=1}^{S} \left(-\frac{1}{2}\pi_s(\alpha - Y_s)^2\right) = -\frac{1}{2}\sum_{s=1}^{S} \left(\pi_s(\alpha^2 + Y_s^2-2\...
- 6,165
8
votes
Accepted
Current knowledge about the empirics of consumer theory
The primary literature concerned with this type of question (at least where classical results break down) is behavioral economics. There's a great general compilation of papers put together by the ...
- 1,040
7
votes
Accepted
Does risk aversion cause diminishing marginal utility, or vice versa?
I think I've found an answer to my question, in this excerpt from Nobel laureate John C. Harsanyi's 1994 paper "Normative validity and meaning of von neumann-morgenstern utilities", presented at the ...
7
votes
Accepted
Envelope Paradox
Here is an "expected utility maximization/ game theoretic" approach to the matter (with a dash of set-theoretic probability). In such a framework, the answers appear clear.
PREMISES
We are told in ...
- 32.9k
7
votes
Accepted
Meaning of $dF(z)$ in expected utility framework
Not all cdf’s have a density function, (for example if $F$ is not differentiable). However, when they do have a density, the notation $dF(z)$ is equivalent to $f(z)dz$. When performing integrals. ...
- 4,188
7
votes
What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?
Junior econ professor here. I saw Ole Peter's work and I was intrigued, so I actually looked into it to see if there was something original/insightful for me to learn. I even run a little simulation ...
- 678
6
votes
How does expected utility theory treat losses?
Gains and losses presuppose a reference point, which is not a feature in standard expected utility theory. In this theory, the only argument in the utility over wealth is $w$, the absolute level of ...
- 15.1k
6
votes
What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?
I’am the guy who wrote the short note that was mentioned in the original question.
You can reach the note here.
https://osf.io/preprints/socarxiv/axkfg/
I got interested in Peter's paper because of my ...
6
votes
Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?
Many people accept the axiomatizations of expected utility as normatively appealing, especially in contexts of pure risk. For people with this view, rational decision-makers should behave in ...
- 10.9k
6
votes
Accepted
Expected value inside a utility function
No, $u_1(x_1-E[x_2])$ is agent $1$'s utility of the expected value, not the expected utility of the value.
Generally $u(E(x)) \neq E(u(x))$. A simple example:
Let $x$ take value $-1$ with probability $...
- 28k
5
votes
Will high computing power substitute the certainty-equivalence assumption?
This is perhaps a good opportunity to point out that the "certainty equivalence" concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in ...
- 32.9k
5
votes
Does risk aversion cause diminishing marginal utility, or vice versa?
The utility function is a representation of preferences, which are traditionally inferred from choices. Preferences come before utility. I would not call the connection between utility and preferences ...
- 928
5
votes
Reverse auction formula
A first price standard and reverse auction are formally equivalent to each other, and the same method can be used to solve both:
First Price Auction
In a first price auction, $n$ bidders choose ...
- 16.8k
5
votes
Experiments contradicting the expected utility model
Picking up my comment under this answer.
One striking issue relevant to decisions not captured by expected utility is the framing effect discussed by Tversky and Kahneman (1981) and others.
In their ...
- 5,170
5
votes
Accepted
Why is the risk premium always positive for risk averse individuals?
Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(...
- 436
5
votes
Accepted
Who is the first one to equate "rational" with "complete and transitive preference"?
As pointed in the comments this was done by Ragnar Frisch. At least Barten and Böhm. (1982) as well as Johansen (1969) attribute these axioms to one of these two publications:
Frisch, Ragnar (...
- 50.1k
5
votes
Accepted
Expected utility theory (Lottery notation)
$$
\left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right)
$$
is the lottery where you get $1000$ with probability $2/100$ and $0$ with probability $98/100$.
The expression
$$
20 \sim \left(...
- 8,682
4
votes
Experiments contradicting the expected utility model
Let me mention another quite well-known one: The calibration theorem by Rabin (2000) and Rabin and Thaler (2002). The idea is that over small stakes individuals must be essentially risk-averse, but in ...
- 5,170
4
votes
Experiments contradicting the expected utility model
Kahneman and Tversky's experiments and many in behavioural economics contradict the existence of a utility function (preferences not complete and transitive), therefore also contradict expected ...
- 928
4
votes
Intuition behind risk premium
There is a typo in the figure that introduces some confusion in the previous answer, which is basically wrong.
Based on the numbers and the figure, the utility is such that $$u=\sqrt{x},$$ so
$$E[u]=\...
- 6,855
4
votes
Risk Premium in the Expected Utility Theory
It is worth noting that the "risk premium" you are talking about is in fact more accurately referred to as the Arrow-Pratt approximation of the cost of a small additive risk. You can approximate it ...
- 69
4
votes
Question about the Ellsberg Paradox in Expected Utility Theory
The short answer seems to be yes your example violates expected utility... It mostly seems to me like a simple transformation of the first example you gave (but you got rid of the red balls).
As ...
- 1,593
4
votes
Accepted
Decision Theory Question: Existence and uniqueness of the certainty equivalent of p
Your notation is a bit misleading: it would be better to write $\mathbb{E}u(p)$ or $U(p)$ for the expected-utility associated with $p$ instead of $u(p)$, and $u(\mathbb{E}p)$ for the utility of the ...
- 3,212
4
votes
Have there been attempts to measure the value of specific taught skills?
Have there been any empirical attempts to estimate the value of being taught specific skills - for example, phonics or solving algebraic equations?
If I may be brazen enough to challenge the basis of ...
- 7,920
4
votes
Accepted
Maximal Allais paradox
One must first distinguish two different senses in which the Allais Paradox can be seen as a "contradiction" of vNM independence; these correspond to the two different interpretations which can be ...
- 642
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