Questions tagged [uncertainty]

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How are research study results on marketing psychology generally interpreted?

I'm getting into marketing. I've been reading books, articles and even research papers on the topic. I'm confused about how to actually interpret information and research study results in this field. ...
kyopa's user avatar
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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 ...
EcoSTUD233's user avatar
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How to solve for the competitive equilibrium in this very lopsided model?

Suppose there's an infinite-horizon pure-exchange economy with 2 agents. Utility function for both agents is $$u(c)=\frac{c^{1-\sigma}}{1-\sigma}$$ The state at $t\geq 0$ is a random variable, $s_t$, ...
Ludwig Gershwin's user avatar
2 votes
2 answers
155 views

Minimal assumption for a “certainty equivalence” exists

Let $R$ be the set of real number. Let $N$ be an infinite set. Let utility $u:R^N\to R$. The utility function is strictly monotonic. My question is, does the certainty equivalence $CE$ exist? Do we ...
High GPA's user avatar
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What are the theoretical approaches to ambiguity?

I'm trying to understand the different approaches that economists took to investigate ambiguity. Two approaches particularly caught my eyes: the model by Klibanoff, Marinacci and Mukerji (2009), and ...
Eddie's user avatar
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1 vote
1 answer
600 views

How do you prove NO difference in Expected Value, between gambling (probable $−$ EV) vs. investing (probable $+$ EV)?

How do you mathematically prove that "From a mathematical expected-value standpoint, there is no difference between gambling (e.g. buying a lottery ticket) and investing (e.g. buying a share of ...
user avatar
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1 answer
113 views

How to decide whether to buy a lottery with a too negative EV, but passable $\Pr($you win jackpot at least once│n plays)?

Daily Keno's too negative Expected Value looks scammy. For all the different wagers of Keno's $10 PICK, the odds of winning jackpot are selfsame : 1 in 2,147181. I computed their EV. Wager Jackpot EV ...
Ethen's user avatar
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-1 votes
1 answer
108 views

Lotteries in an equilateral triangle

A variable can take 3 values, each represented by a vertex of an equilateral triangle. Every point in the triangle is then a lottery over the vertices. How are the elements of each lottery related to ...
android16.5's user avatar
2 votes
1 answer
131 views

Willingness to sell a lottery ticket vs. willingness to buy a lottery ticket

I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would ...
papagena's user avatar
2 votes
0 answers
38 views

Does local non-satiation hold for this problem?

I am getting some confusing results solving this problem: $max_{c_0\geq0, c_1\geq0} \bigg\{EU = R(1-c_0) [p t_1 + (1-p) c_1^{-2} t_2] \bigg\} ~ s.t. ~c_0+c_1 \leq 1$ where $p$ is the probability of $...
L1234's user avatar
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CARA risk-parameter estimation for discrete data as in Holt and Laury (2002)

I have a dataset with around 40 participants who choose between a pair of lotteries A or B while the probabilities of prizes change. This setting is similar to that in Holt and Laury (2002): Risk ...
Juustomies6's user avatar
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0 answers
47 views

Problem on VNM utility

Preferences are represented by the function $u(w) = √w$ . An investor has 5000 dollars that can be invested. Investing $X ∈ [0,5000]$ he will receive $r_H X$ in addition to W with probability $P$ and ...
Laney's user avatar
  • 31
2 votes
1 answer
54 views

Lower bound for the utility in a decision problem with uncertainty

Model Consider a single-agent decision problem with uncertainty. A decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. $\mathcal{Y}...
Star's user avatar
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1 vote
1 answer
81 views

Arrow-Debreu Market with Uncertainty

I am reading some lecture note on stochastic macro model. Say an endowment economy with agent $i=1,2$, who receive the random endowment each period $e_{t}^{i}\left(s^{t}\right)$ where $s^{t}=\left(s_{...
Alalalalaki's user avatar
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1 vote
1 answer
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Expected utility function and Full insurance

Bob is an expected utility maximizer with utility function $u(x) = −e^{−ax}$, where $a > 0$ is a parameter. Bob has wealth $w$. There are two states of the world, a good state and a bad state. The ...
user40996's user avatar
2 votes
1 answer
315 views

Von-Neumann vs Bernoulli Utility? Do properties of Bernoulli translate to VNM?

This is for a HW question but I am not asking on how to solve the question, just a conceptual question. According to my understanding, A Von-Neumann Utility function represents preferences over ...
Kinno's user avatar
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1 answer
141 views

Arrow debreu equilibrium or Radner equilibrium and spot prices

Suppose there are 2 states, 2 goods and 2 consumers and consumers have identical expected utility function: $U^i (x)= \sum_{s=1,2} \pi_s (\ln x_{1s}+\ln x_{2s} )$ where $\pi=(1/3,2/3)$. Endowments are ...
guest's user avatar
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4 votes
1 answer
104 views

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 ...
High GPA's user avatar
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0 answers
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Risk Aversion under Worst Case Utility Representation

The preference relations (≿A and ≿B) over lotteries is defined as: p ≿ q iff min{v(z) : p(z) > 0} ≥ min{v(z) : q(z) > 0} Under what conditions can you say that ≿A is more risk averse than ≿B?
archana's user avatar
0 votes
1 answer
440 views

Negative certainty equivalent

Let us consider an agent of initial wealth $w_0$ whose utility function is $u(x)=\sqrt{x}$. This individual faces a risk of loss $Z$ which occurs with probability $p$. It is assumed that $w_0=60000$, $...
weldon's user avatar
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5 votes
2 answers
301 views

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 ...
Rumi's user avatar
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2 votes
1 answer
57 views

Volatility indexes

I want to use a volatility index as a measure of economic policy uncertainty. The index that I want to use is CBOE Volatility Index: VIX, but I don't know if I only can use this for US or if I can use ...
waka 's user avatar
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2 votes
2 answers
336 views

Drawing a Probability simplex

There are 3 possible payoffs - \$4, \$9 and \$36. The utility function for these payoffs is $\sqrt x $. I have to find all the lotteries preferable over getting $9 with probability 1 in a probability ...
Kritika's user avatar
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1 vote
1 answer
152 views

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 $\frac{1}{2}$ ...
Mrnobody's user avatar
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0 answers
66 views

comparing two lotteries

Suppose the prize space (in dollars) is $\mathbb{Z}$ = {1, 2, 3, 4, 5, 6, 7, 8} and consider choices by an agent whose preferences (over lotteries) satisfy the von Neumann-Morgenstern axioms. A risk ...
Mrnobody's user avatar
1 vote
1 answer
130 views

Choice under uncertainty

I am practising past micro economics questions from the internet and I am not sure how to proceed with this question: Imagine a situation where a risk averse agent has positive wealth(w) and may face ...
Gill's user avatar
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2 votes
0 answers
40 views

Deducing beliefs from choices when the Savage Axioms are true

We know, that given a set of possible outcomes $X$, a set of states of nature $\Omega$, and the set of all acts from $\Omega$ to $X$, if a DM has rational preferences over the acts and if the Savage ...
Ishan Kashyap Hazarika's user avatar
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1 answer
71 views

Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
j3141592653589793238's user avatar
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0 answers
52 views

Pure Nash equilibrium in bidding game?

According to the answer key for a problem set, there is no pure strategy Nash equilibrium in the following problem. Yet I can't see why not. Could it be an error in the answer key? Here's the problem: ...
Nomista's user avatar
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1 vote
1 answer
249 views

Comparing & contrasting decision problems and normal games

I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.
Wivaviw's user avatar
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1 vote
0 answers
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Choice under Uncertainty: Relation between the certainty equivalent and the coefficient of relative risk aversion

That's my question! Propositon 6.C.4 (MWG (1995)): The following conditions for a Bernoulli utility function $u(\cdot)$ on amounts of money are equivalent: (i) $r_R(x,u)$ is decreasing in $x$. (iii) ...
Rômullo Eduardo's user avatar
2 votes
1 answer
90 views

Uncertainty and Pareto efficient policies

There are two economic agents $i\in \{1,2\}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $x\in R$ and $b_{is}\in R$ is bliss point of $i$ in state $s\in\{1,2\}$. Assume $b_{1s}\lt b_{2s}$...
Maybeline Lee's user avatar
3 votes
0 answers
62 views

Epstein zin and resolution of uncertainty

I'm reading Simon Gilchrist's notes here. I understood everything until and including page 14, where it reads $$\frac{W_h^{1-\rho} + W_l^{1-\rho}}{2} \geq \frac{c_h^{1-\rho} + c_l^{1-\rho}}{2} $$ and ...
user1691278's user avatar
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0 answers
91 views

Proof of certainty equivalence

The questions say two lotteries are denoted L1 = (0.3,0.7,0.0) and L2= (0.9,0.0,0.1) and denote c(L1) and c(L2) the certainty equivalents of those two lotteries. Then prove L1 ≻ L2 if and only if c(L1)...
Mike Edison's user avatar
2 votes
1 answer
777 views

Can the Certainty Equivalent be negative?

I am questioning if the CE of a lottery can be negative? For me it doesn't make much sense by definition. I encountered this problem on the following exercise: Imagine a case where we have a lottery(...
Gonçalo Gameiro's user avatar
4 votes
1 answer
63 views

Lotteries = probability distribution?

Are "lotteries" in the model for choice under uncertainty not just probability distributions?
Xenusi's user avatar
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1 vote
0 answers
42 views

Term for risk AND ambiguity

This question is related to References for particular definitions of risk and uncertainty, which offers an excellent description of risk and uncertainty. Just as a recap: Knight (1921) described risk ...
Karl A's user avatar
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1 vote
3 answers
741 views

Can we compare risks of lotteries?

I understand the concepts of risk-aversion, risk neutrality and risk-attraction. I wonder if it possible to compare risks between two lotteries without giving the utility function. For instance, Let ...
Alex Wang's user avatar
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3 votes
1 answer
129 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: $$...
David Bowman's user avatar
-1 votes
1 answer
302 views

How to prove the relationship between the expected value of a lottery and its certainty equivalent?

Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent). (Definition of $CE$: the ...
Aqqqq's user avatar
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2 votes
1 answer
310 views

Conditions for Radner Equilibrium

This is definition of Radner Equilibrium from Microeconomic Theory (Mas-Collel, Whinston and Green - Third Edition). I'm confused about two conditions: $\sum_k q_k \cdot z_{ki} \le 0$ (in yellow) The ...
Incognito's user avatar
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1 answer
37 views

Existence of optimal strategy in a choice problem with uncertainty and information structure

Consider a decision maker choosing an action, $y$, from the finiteset $\mathcal{Y}$, possibly without having complete information about the state of the world. More precisely, let $V$ be a ...
Star's user avatar
  • 436
0 votes
1 answer
53 views

Robust predictions in single-agent decision problem with uncertainty

I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ...
Star's user avatar
  • 436
0 votes
1 answer
57 views

Optimal strategy in a single-agent choice problem under uncertainty

Consider the following single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{v})$. First, ...
Star's user avatar
  • 436
1 vote
1 answer
58 views

Budget constraint in Radner Sequential Trade Equilibria

Suppose that $q$ is a k-tuple vector of prices for the k assets whose quantities are given by the k-tuple $\theta$. I have just read that in the Radner Sequential Trade Equilibrium (not sure if this ...
David's user avatar
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2 votes
0 answers
52 views

Dominated lotteries in CPE

I have been looking into expectation-based loss aversion following Kőszegi-Rabin (2005, 2007). In particular, I find their choice-acclimating personal equilibrium (CPE) interesting, but it has a ...
Bayesian's user avatar
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2 votes
1 answer
483 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?
John Stern's user avatar
1 vote
1 answer
365 views

Archimedean but not mixture continuous

In the context of preferences on a set of lotteries on a finite set $X$, what is an example of a preference that is independent, Archimedean but not mixture continuous? I know the mixture continuous ...
yurnero's user avatar
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3 votes
1 answer
229 views

Why Certainity Eqivalence in PIH only holds for quadratic utilities

In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was ...
Jhonny's user avatar
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2 votes
1 answer
358 views

Question on uncertainity

Please imagine that Nicole is uncertain of her future wealth. Her wealth in the bad state of the world is zero. Her wealth in the good state is $w>0$. Each state is initially equally likely. ...
b11bb's user avatar
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