# Questions tagged [decision-theory]

For questions regarding formal decision problems. In contrast, questions involving strategic aspects (where the solution depends on the behavior of others) are discussed in game theory.

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### Applying Markov Decision Processes to an arrival forecasting problem

I have the following problem and I'd like to know if it's something that was already studied in the literature or not. I'm not sure about the naming conventions either. I have a system $S$ that can ...
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### Which branch of math theory could solve the task?

Imagine that we have a value $s_i = f(s_{i-1}, x_{i-1})$, reccurent formula $s_i$ with parameter $x_i$. $x_i$ values depends on $x_0$ and each $x_i$ is calculated in a diffenrent way. I guess it is ...
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### What to do when in Coombs voting method there two equal weights for candidates to be elimenated?

I've read about Coombs method on Wikipedia. I understand that we eliminate candidate with the most last-place votes. But what do we do when, for example, two candidates A and B have equal number of ...
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### Question about Bayes risk and best rule Bayes

I'm start to learn Decision Theory and I'm trying to solve (analytically) the exemple 2 from Berger, pag. 5-6 (James O. Berger - Statistical Decision Theory - 1980). I can't understand the result (how ...
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### Which act should be chosen according to the principle of maximizing expected monetary value ( EVM )?

Assume that the decision maker's utility u of money is linear. Consider ...
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### Is it possible to get no solution from an optimal stopping problem

I recently read about the 37-percent rule as the solution to the secretary problem. It says To have the highest chance of getting the best applicant from a pool of applicants, you should interview ...
1 vote
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### Total Utility Value Composition of Different Utility Functions

Let's suppose we have a variable $x$ with a domain $X \in [0,1000]$ and two utility functions $uf_1(x)$ and $uf_2(x)$ that describe the utility of $x$ with respect to two different properties. We ...
1 vote
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### How to find a utility function

The choices are of the form $(x; y)$ where $x$ represents the amount of time you have left to live, say anywhere from $0$ to $50$ years, and $y$ represents the amount of time you have left to work, ...
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### Decision Analysis on game - Y vs L uncover pattern

I am trying to understand the logic of the community in choosing a specfic strategy to maximize profit in a game. The game can be described as follows: Every ticket has nine spaces, with a number ...
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### Need some clarification on what "decidability" means.

[I am relatively new to computability theory, so please try to avoid complicated jargon except as absolutely necessary. Thank you for your time!] So I get that a decision problem is decidable iff ...
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### Is the question whether the value of a given definite integral has a closed-form decideable?

Suppose, we have a definite convergent integral (possibly improper) with an elementary function as an integrand. Is there an algorithm deciding whether the value of the integral has a closed-form ...
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### What are some techniques of constructing a good utility matrix?

A utility matrix is considered to be subjective and arbitrarily defined. Therefore, we run the risk of over-emphasizing or under-emphasizing the possible alternatives. Are there ways to design an ...
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### Bayes risk and Bayes decision

We are considering a sample of size $n$ from an exponential distribution, with parameter $w >0$. We wish to produce an estimate for $d$, for $w$ , with loss function: $L(w, d)=w(w-d)^2$ The prior ...
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We record measurements of an appartus every day. If apparatus doesn't break (it has probability equal to $1-p_2$), it will measure zero with probability $p_1$. If apparatus breaks (probability $p2$), ...