# Questions tagged [probability]

A branch of statistics that studies the likelihood of uncertain events occurring.

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### About The Bayesian Conditional-Probability Systems in Myerson's Game Theory: Analysis of Conflict

I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his Bayesian conditional-probability system. The Bayesian conditional-probability ...
1 vote
37 views

### Understanding the notations in Bayesian game definition

I am having trouble understanding the definition of a Bayesian game based on the following definition from class. I would appreciate it if you could explain the notations and overall meaning for point ...
22 views

### transition probabilities from a AR(1) stochastic process

I have a stochastic volatility model for commodity price which follows an AR(1) process: ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1) σt − μ = ρσ(σt−1 − μ) + ηεt εt ∼ IID(0, 1) ...
183 views

### Deriving an equation in Banerjee "A Simple Model of Herd Behavior" (1992)

I am reading "A Simple Model of Herd Behavior" by Banerjee (1992). A short summary of the model is the following. There is a probability $\alpha$ that each person receives a signal telling ...
1 vote
93 views

### Probability for Economics

I need to learn ASAP on the list of topics: Multivariate Distribution, discrete and continuous random variables; integration and expectation; law of large numbers and central limit theorem, confidence ...
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### Estimating excess probability

I have three players A,B,C, where C ideally functions as a baseline. They play different games (not against each other) and I can observe their win probability, for example P(A wins in game I) = 90%, ...
49 views

### Third price auction from Auction Theory by Krishna, Order statistics

Notation: $Y_1$: Highest order statistics of $(N-1)$ players' valuation. $F_n^M:$ The distribution function of the highest $n$th order statistics of $M$ players. $f_n^M:$ The density of the highest $n$...
115 views

### What does it mean when I say that CDF is bounded away from 1?

Suppose $\theta \in [\underline\theta, \bar\theta]$ is distributed with CDF F(.). What does it mean when I say that this F is bounded away from 1? Does it mean that F can never take the value 1 in ...
60 views

### Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?

In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies. In a Correlated Equilibrium or a Coarse Correlated ...
1 vote
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### Understanding the properties of extensive form games

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. To some point they refer to the following two properties $P$ is a mapping ...
1 vote
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1 vote
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### 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
61 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 ...
### 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 ...