Questions tagged [probability]
A branch of statistics that studies the likelihood of uncertain events occurring.
78
questions
3
votes
1answer
17 views
Expected payoff calculation difficulty in the Bayesian environment of Bergemman and Morris
Suppose that we have two states of the world equally likely to occur, and say $\psi$ is the common prior of the state $\theta\in\Theta=\{G,B\}$. The types of the players are given by the following ...
2
votes
0answers
37 views
Bayesian update in the beliefs about the signals
Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
0
votes
0answers
25 views
The most used probability distributions in moral hazard models?
I'm engaged in making a variation of the canonical moral hazard model, but I need some examples of probability distributions to make some simulations and graphs. What are the probability distributions ...
0
votes
0answers
23 views
Questions about the definition of a protocol
The following definition is from this paper about protocols of communications (definition $2.4$ in the paper). You can check the paper for more details and previous of my questions.
$\textit{...
1
vote
1answer
20 views
How to compare investments with different risk and expected return?
Supposing I can choose to invest money in several different investments, each having
risk $\sigma_i$, for example, calculated as standard deviation
and expected return $r_i$
let's assume they have ...
3
votes
1answer
67 views
Mechanisms of communication in game theory
In the spirit of the previous question that I have done, here considering the paper here I am trying to make the matching definition $2.2$ here.
I will give two definitions and I would like to clarify ...
5
votes
1answer
133 views
Difficulty in understanding the notation related from probability theory with game theory
The question that I have is a little technical and it has to do with the notation and the combination between some mathamatical properties in the probability theory of information economics.
Say $\...
1
vote
1answer
25 views
What is the meaning of the support set in game theory?
What is the meaning of the support set in game theory? I have seen it, in many papers, however none there explains how did they find it or why did the define it in a specific way. I understand that ...
5
votes
2answers
104 views
Olivier Gossner - Secure Protocols or How Communication Generates Correlation
The paper of Olivier Gossner in Security Protocols in 1998 has some definitions that confuse me too much. I will cite here these definitions and my questions and I hope someone is familiar with these ...
2
votes
0answers
36 views
In economics, what variables do we usually assume to follow an exponential distribution?
In economics, what variables do we usually assume to follow an exponential distribution? I would like as many examples as possible, and it would be great if you have a rationale(economic reason or ...
0
votes
0answers
37 views
Multinominal logit regressions - marginal effects
I am running a multinominal logit regression with five dependent variable categories: "I disagree fully", "I disagree", "Neutral", "I agree" and "I agree ...
1
vote
1answer
31 views
Interpretation of multinominal logit regression (Stata)
I have a few questions about mlogit. I have a set of independent variables and a categorical, but ordered, dependent variable with three categories (Disagree, Neutral and Agree). The assumptions for ...
1
vote
0answers
16 views
Question on the choice of boundary in the CUSUM test when we make some resampling
Question on the choice of boundary in the CUSUM test when we make some resampling
We are considering to make a CUSUM test for some economical time series $𝑋=(𝑥_1,..,x_n)$. Suppose 𝑋 contains many ...
0
votes
1answer
27 views
Expected value of order statistics for uniform distribution
I have $X$ ~ $U(0,1)$ interval.
Let n=2, i.e. $X_1 < X_2$
I have to calculate the expected value of ${X_2}^{m/(1-m)}$.
Where, $0≤m≤1$
I want to confirm if I have calculated it correctly?
$$\int_0^1 ...
0
votes
0answers
21 views
Probability transition matrix as a function of the variance in Matlab?
I am working on Probability transition Matrix on Matlab. I Have say 5 points (states) of discretized productivity grid. I would like to have two matrix of probability transition subject to the ...
0
votes
1answer
54 views
Integration by parts with CDF
I am told that the following equality follows from integration by parts:
$$\int_{R-k}^{1}(\theta-R)dG(\theta)-G(R-k)k=\int_{R-k}^{1}(1-G(\theta))d\theta-k$$ Where $R>k>0$ and $G$ is the CDF of $\...
0
votes
1answer
48 views
Is it worth betting on this case?
Let's imagine a coin-flip game, which uses an unbiased coin.
Starting with X dollars, your total increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. ...
1
vote
1answer
100 views
Show that conditional variance of error in linear probability model is heteroskedastic?
I have a problem that asks me the following:
" Consider the linear probability model, in which we specify the
regression equation to be linear in X,
E(Y |X = x) = Pr(Y = 1|X = x) = x'β
We can ...
3
votes
2answers
108 views
How to average CDFs of one variable across years
I have wealth-to-income data for 10 years. I computed the cdf of this variable in each year.
Now I'm trying to average the cdfs across years. In each each, the number of observations is different.
...
3
votes
2answers
90 views
How to approach rigorous probability theory from an economics background?
I am attempting to read around the theory of probability theory from the ground up, coming from a background of economics I have little experience in set/measure theory, whilst I am not new to ...
4
votes
1answer
49 views
Average ability conditioning on having accepted an offer
There is a continuum of workers between 0 and 1. These have ability $\alpha\sim U[0,2]$. A firm offers them a salary $v$ and has profits
$$
\pi = (\rho \alpha-v) n(v)
$$
where $n(v)$ is the fraction ...
3
votes
0answers
35 views
Estimating probability of Central Bank's interest rate changes
Recently, I came across this article, which offers a simple model for estimating the probabilities of interest rate cut/hike from a central bank. This is done by using market data, especially normal ...
0
votes
1answer
108 views
Risk neutral probability for each of 3 states
I need help to find the risk-neutral probability for states 1,2 and 3
I have two stocks: A and B.
The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3);
The ...
3
votes
1answer
67 views
Modelling involving sum of random variables: Simple CDF?
This question emerges from a project in microeconomic modeling.
I have $n$ agents receiving noisy i.i.d signals $s$.
In my model, a situation of interest occurs when the average signal across $n$ ...
3
votes
1answer
89 views
Intertemporal choice with possibility of death
Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$...
0
votes
1answer
133 views
Expected Utility and Jensen's Inequality
Consider two random variables (costs and valuations) distributed $v\backsim G(.)$ and
$c \backsim F(.)$ with pdfs $g(.)$ and $f(.)$. Let the supports of $c$ and
$v$ be $[x,y]$. Let $x<a=E(v)<b&...
1
vote
1answer
63 views
Is the set of optimal strategies convex in a single-agent decision choice problem?
EDITED with insights from the comment below.
Consider a decision maker who has to choose an action among $\mathcal{Y}\equiv \{1,2,...,L\}$. The payoff from choosing action $y\in \mathcal{Y}$ depends ...
1
vote
0answers
60 views
Assessing risk in a decision problem with repeated toss
The problem starts at time t0.
At each time step, the participant can choose to opt out and claim a loser's reward Rl.
At each time step, the participant has a probability p to win a winner's reward ...
0
votes
0answers
44 views
Rate of convergence and asymptotic dominance in $\Vert x \Vert \gg \Vert(\hat\beta-\beta)\cdot u\Vert $
Let $\Vert A \Vert$ denote the spectral norm of a random matrix. Let $x$ and $u_k$ be N$\times$T matrices. Denote $\beta \cdot u = \sum_{k=1}^K\beta_ku_k $, where $\beta$ is a K-vector and $\beta_k$ a ...
1
vote
1answer
47 views
Probability of the event knowing that I received no informations
First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting.
I have a particular informational framework ...
6
votes
3answers
5k views
Type - I Error & Type - II Error: Pregnancy test analogy - is it legit?
I found this picture in my stats book but I'm now confused to what 'positive' and 'negative' is referring to.
As seen in the table below, Type 1 error is the error that its H0 is actually true but ...
3
votes
1answer
280 views
Is First Order Stochastic Dominance (FOSD) relation convex?
A convex relation is that $x\succeq y$ implies $\alpha x+(1-\alpha)y\succeq y$.
Let $>_{FOSD}$ be $\succ$, is the FOSD convex? Intuitively it seems convex.
5
votes
0answers
154 views
How to interpret the proof that information cascades will form?
I am reading the 1992 paper of Bikchandani, Hirshleifer and Welch on information cascades. They claim and prove that, given an environment of sequential decision making, an information cascade will ...
1
vote
0answers
76 views
Global games: How to derive posterior with uniform prior and signal
I have access to some lecture notes on Global games (following the model of Carlsson and van Damme (1993)) showing how to derive the players posterior beliefs. But I don't really grasp how players ...
2
votes
1answer
129 views
Best-responding to a stochastically higher distribution of bids
In Auction Theory, Krishna writes that:
a bidder who faces a stochastically higher distribution of bids–in the
sense of reverse hazard rate dominance–will bid higher
(This follows the proof of ...
1
vote
0answers
16 views
Expectation conditional on a sum of random variables
The setting is a simple OLS regression where the true model has regressor $x$ and error term $u$, but we can only measure $\bar{x}=x+v$ where $v$ is iid with mean 0.
According to the textbook:
$\...
3
votes
0answers
56 views
Mean Field/Differential Game and Measurability
Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
0
votes
1answer
22 views
When to invest into additional products?
This is a very applied question so I hope it's the correct adress here for it:
I'm running a small entertaining business for virtual reality experiences. Investment was about 120 k. I now build it ...
0
votes
2answers
1k views
Find all of the Pure and Mixed Strategy Nash Equilibria [closed]
When I do the basic calculations for mixed probability, I get that the Column player always plays B. However, I am getting a negative probability for the row. Any help is appreciated.
1
vote
0answers
26 views
How to determine the default probability of a county in a bond that is not in its native currency?
Consider the following case:
Country P uses the currency Euro and gives p percent interest on a one year bond issued in Euro.
Country Q uses the currency TL and gives q percent interest on a one ...
2
votes
2answers
44 views
understanding the proof of stochastic dominance.
$\int_a^b u(x)dF(x)$ (1)$ = u(t)F(t)|_a^b - \int_a^b F(t)u^\prime(t)dt$ (2)$ = u(b)-\int_a^b F(t)u^\prime(t)dt$
$= u(b)-(\Phi(t)u^\prime(t)|_a^b-\int_a^b \Phi(t)u^{\prime\prime}(t)dt=u(b)-\Phi(b)u^\...
2
votes
1answer
35 views
Dimensional analysis for the qdf/quantile function corresponding to the pdf/CDF for the size distribution of income
I have previously posted a very similar question on Stackoverflow, but based on responses there I have decided that the real nub of my question is economic. I will give a longish introduction, mainly ...
5
votes
1answer
151 views
What exactly is/How exactly do we interpret the binomial model's Radon-Nikodym derivative?
Related: Lewis' triviality result?
As I recall the one-step binomial model goes like this:
The time periods are now $t=0$ and later $t=1$.
We have
2.1. a stock that pays off $u$ for going up or $d$...
1
vote
0answers
36 views
Marital status determinants
I am looking for the researches that have studied factors influencing marital status probability. I need them for citation purposes. After looking for a long time I have not found anything. So I need ...
5
votes
1answer
167 views
Higher order beliefs and coherency in game theory
I am reading about the higher order beliefs. Before getting into the formal definitions, I will define some common terminology which I will need for the formal definitions.
If $X$ and $Y$ are two ...
0
votes
1answer
33 views
Is lowered probability of spending equals savings? [closed]
This a really basic one and logic says: Yes given enough iterations.
But I am looking for validation
Situation: There is a 7% probability of expenses of 1000 occurring. I have a tool that then ...
9
votes
1answer
232 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 ...
2
votes
3answers
78 views
Investment and probability
Being a mathematician, I am familiar with probability calculations, but I need to ask a question related to investments and probability, and how this is handled seen from an economics view.
Given a ...
1
vote
2answers
75 views
If an item is rarer than others, is it that much more valuable?
Say I am selling a pack of trading cards, and there are 5 cards inside. Four of these cards are basic cards, but the last card has a 1:10 chance of being a special insert card.
Does the fact that the ...
11
votes
1answer
186 views
second order stochastic dominance without the same mean
Let $F$ and $G$ be two distributions with the same mean. $F$ is said to second order stochastically dominate (SOSD) $G$ if
$$\int u(x)\mathrm dF(x)\ge \int u(x)\mathrm dG(x)\tag{1}$$
for all ...
