Questions tagged [uncertainty]
The uncertainty tag has no usage guidance.
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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 lotteries from $\Omega$ to $X$, if a DM has rational preferences over the lotteries and if ...
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1answer
46 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 ...
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33 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:
...
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1answer
41 views
How to Represent as a Payoff Matrix
I'm trying to represent the following as a pay-off matrix.
I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
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1answer
210 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.
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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) ...
2
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1answer
58 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 $b_{1s}\lt b_{2s}$...
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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 ...
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0answers
37 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)...
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1answer
399 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(...
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1answer
52 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
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33 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 ...
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3answers
280 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 ...
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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:
$$...
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1answer
151 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 ...
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1answer
18 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 ...
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1answer
46 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 ...
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1answer
48 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, ...
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0answers
33 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 ...
2
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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?
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0answers
101 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 ...
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1answer
132 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 ...
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1answer
318 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. ...
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1answer
59 views
Indiference between two lotteries
Suppose that a binary relation satisfies only:
Independence axiom: $L≿L′⟺α\circ L+(1−α)\circ L′′≿α\circ L′+(1−α) \circ L′′$
Reduction to simple lotteries: For all $g$, $g~g'$, $g'$ is the simple ...
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2answers
291 views
Uncertainty in an unfair gamble
If a risk averse person is given the option of a certain amount of 2000 or playing a lottery game giving him 10000 with 25% probability, and 500 with 75%, then what would he do ?.
The bet here is not ...
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1answer
72 views
Profit maximization under uncertainity
I have a seller say S and I have a buyer say B. Buyer’s willing to pay is equal to x which is private information. But Seller believe that it falls in the range [0,x1]. Seller’s belief distribution is ...
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1answer
881 views
What exactly is certainty equivalence in the context of DSGE models?
I keep reading about certainty equivalence in the context of DSGE models.
I understand that it has something to do with "Getting rid of the expectation operator", but I'm not entirely sure? ...
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1answer
57 views
A growth model with regime switch
I have a very general question. I am reading this paper :
http://www.webmeets.com/files/papers/eaere/2015/177/Discounting-HelsinkiBlind.pdf
There is a catastrophic event probability and after the ...
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5answers
879 views
References for particular definitions of risk and uncertainty
I have some doubts about risk vs. uncertainty. I have read the thread "What is the difference between risk, uncertainty and ambiguity" and have skimmed through Knight's "Risk, Uncertainty, and Profit" ...
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2answers
178 views
Help with a choice under uncertainty exercise [closed]
Let $u$ and $v$ be utility functions (not necessarily VNM) representing $\succsim$ on $\mathcal{G}$. Show that $v$ is a positive affine transformation of $u$ if and only if for all gambles $g^1, g^2, ...
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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 ...
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1answer
348 views
Inc Linear Transformation of Bernoulli Utility
According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation.
What is the significance of this proposition?
The part I ...
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1answer
75 views
Consequentialist View of Risk
In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker.
From philosophical view, ...
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8answers
3k views
Would insurance plan be necessary if we had instant access to credit?
Assuming one could instantly have access to an loan to cover his recent loss/accident at an affordable interest, would it make sense to pay premium for an insurance plan?
I was thinking that it would ...
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1answer
187 views
Is car accident/theft a fair bet? [closed]
A person with a current wealth of 100,000 who faces the prospect of a 25% chance of losing his or her 20,000 automobile through theft during the next year. Since there is no upside to this event and E(...
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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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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 ...
4
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1answer
102 views
What sort of impact would one expect on investment as a result of an approaching election?
I am looking to observe and possibly quantify private investment during election periods.
I am interested in any studies, particularly empirical, which discuss the impacts elections can have on the ...
2
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1answer
287 views
Constraints on a symmetric pareto allocation under uncertainty
I've been trying to figure out how the author came up with the constraints for this liquidity model in a textbook I'm reading.
details: http://imgur.com/TpVjg4w
$U = \pi_1u(C_1) + \pi_2u(C_2)$ where ...
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
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
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 ...
5
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1answer
482 views
Independence axiom of lottery when $\alpha \ge 1$
When studying preference over lotteries we learned the independence axiom which goes like this:
The preference relation $\succsim$ on the space of simple lotteries $\mathscr{L}$ satisfies the ...
2
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0answers
406 views
Probability of states of nature
I've been given the following question and would really appreciate any help on part a. I've looked over all of my resources for this course and we have always been given the probability of the ...
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2answers
284 views
Economics of forgetting
I'm interested to know economic justifications of forgetting in various fields.
On example is Green and Porter(1984). To sustain a Cartel, Cartel members have incentive to forget deviations in a ...
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1answer
60 views
What's the status on uncertainty shocks?
Bloom (2009) analyzes the impact of uncertainty shocks, and Bloom et al (2014) propose a business cycle model based on these shocks.
It seems to be a young field, but is there any consensus on ...
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1answer
91 views
Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
I'm trying to understand the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies." In a part in the paper, Hansen introduces a long-...
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2answers
224 views
How could the Euro zone be broken up in an ordered way?
Let’s assume that the members of Euro zone all agreed that it would end in 18 months time with each country getting its own currency.
What process could be put in place to allow this to happen ...
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2answers
903 views
How is momentum justified as a common risk factor?
Momentum as a common risk factor?
This question is partly a follow-up to another question found here. In this other question it was noted in momentum is difficult to explain as a common risk factor ...
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1answer
678 views
What is the advantage and disadvantage of fiscal illusion policy in terms for the financial market?
What is the advantage and disadvantage of fiscal illusion policy for the financial market?
Fiscal illusion suggests that when government revenues are not completely transparent or are not fully ...
