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.

learn more… | top users | synonyms

1
vote
1answer
53 views

How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
0
votes
0answers
18 views

Modeling a multiple criteria decision problem

Sorry for the generic-sounding title. I am currently tasked to solve a decision problem. Currently there are two factors that I must consider before making the decision. Suppose a customer walks ...
0
votes
0answers
24 views

Measure Theory vs. Decision Theory - problem classification

I am having trouble classifying my problem, and I am seeking some guidance on book advice. I don't know if I have measure-theory problem and/or a decision-theory problem (or other field). I want to ...
1
vote
0answers
21 views

Name of decision method in which probability of taking an action is exactly past successes / past attempts, while alternative actions normalize

The probability of choosing among options $X_1$, $X_2$, $X_3$, $...X_n$ is initially uniform, i.e. $P(X_j)=1/n$. On choosing $X_j$, either success or failure will occur (with unknown probabilities, ...
0
votes
0answers
22 views

Characterizing relation “ has no less information than” between information systems represented by Markovian matrices

I'm reading this note on Blackwell's theorem which establishes the monotone relationship between the information in a information system a decision maker faces and his expected welfare. An ...
0
votes
1answer
29 views

Natural Decision Problem not in PTIME

Are there any natural decision problems which are guaranteed not to be in $\mathsf{PTIME}$? Preferably natural graph problems like $\mathsf{CLIQUE}, \mathsf{VERTEXCOVER}$ etc. (However, they would be ...
0
votes
1answer
40 views

Maximum-Value Secretary Problem

Background: The classic secretary problem has the simple solution of rejecting the first 1/e applicants and then selecting anyone who was better than the best in the rejected set. However, in the ...
5
votes
1answer
62 views

Is this a problem that has already been solved?

I have a question paper with $n$ True/False questions and I don't know the answer to any of those questions. My objective is to find the answer key of the question paper. All I have is a machine which ...
14
votes
3answers
3k views

Can I use the “Secretary Problem” to find the worst candidate, too?

As you know, we use the "Secretary Problem" to choose the single best candidate. Now I would like to know can we use this rule to find the worst candidate, too? If yes, how to accomplish this?
2
votes
1answer
138 views

Would a risk averse agent ever accept gambles with negative expected value? [closed]

Consider a risk-averse agent (his utility for money is strictly concave) that maximizes expected utility. Would such agent ever a accept a gamble whose expected value is negative? (e.g. think of state ...
2
votes
0answers
32 views

Decide whether a function has an elementary indefinite integral without determining it!

Risch, who developed the algorithm in 1968, called it a decision procedure, because it is a method for deciding whether a function has an elementary function as an indefinite integral; and also, if ...
1
vote
0answers
65 views

How to test a flash light.

Let us say you have a flash light. At full charge, it can last for 2 hours (or $T$.) Right now, it charge is a random variable $C$ which has a uniform distribution (or distribution $D$.) You may turn ...
0
votes
0answers
62 views

MDP problem - How is the expected cost calculated?

I have been stuck with a problem for a while regarding Markov Decision Processes for a Policy improvement algorithm. Assume that I have probabilities for certain states to evolve the system into, ...
0
votes
0answers
34 views

Decision Making Algorithms - Chaos Theory

I'm doing research on decision making algorithms on robotics. And recently I've read a lot of about Chaos Theory. I've searched all over the web, in IEEEXplore, ACM Digital Library, but can't find any ...
1
vote
0answers
44 views

Classification problem: admissible rule is a Bayes rule for some prior $\pi$

I have a classification problem where I want to place an observation $X$ into a population described by a pdf equal to either $f_1$ or $f_2$. Given $P_{f_i}(\frac{f_1(X)}{f_2(X)}=j)=0$ for all $j\in ...
4
votes
1answer
118 views

Maximising probability for financial advice

I have the following problem: A financial advisor tries to impress his clients if immediately following a week in which the ftse index moves by more than $5\%$ in some direction he correctly ...
3
votes
1answer
104 views

Mistake wikipedia article on St petersburg paradox?

I suspect that there is a mistake in the wikipedia article on the St petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
2
votes
1answer
118 views

Question on the equivalence of behaviour strategy and mixed strategy for a player with a single information set

Prove that if a player in an extensive-form game has only one information set, then his set of mixed strategies equals his set of behavior strategies. This is the exercise $6.4$ on page $246$ in ...
3
votes
6answers
149 views

When to stop doubling down?

My question is similar to this one but very specificly different When to stop in this coin toss game? Imagine a game where you would start with $100. Every time you can roll a die (d6), if it is 1-5 ...
1
vote
1answer
62 views

simultaneous probability elicitation from multiple agents without an exogenous banker

A proper scoring rule is a function $f:[0,1]\times\{0,1\}\to \Bbb R$ such that, if a subject will receive a reward of $f(x,0)$ for reporting his estimate of the likelihood of an event as $x$ if the ...
0
votes
1answer
47 views

Decision theory question about selling a house

I have a real world problem and I was wondering if you guys have any nice insight on the best way to solve it mathematically. I'm not sure there is a decisive solution, but it would be nice to have a ...
2
votes
4answers
109 views

death as a cost in decision theory

If I presented with an optional task for which I have an outcome independent investment $I$, a probability of success $P$ and a reward for success $R$, then I chose to undertake this task iff $PR > ...
0
votes
0answers
34 views

Inadmissibility of constant decision rule

My loss function is the squared error loss, $L(\theta,a)=(\theta-a)^2$. Suppose $X\sim U(0,\theta)$ given $\Theta=\theta$. I need to show that the constant decision rule $\delta(x)=c$ is inadmissible ...
3
votes
1answer
139 views

Formal Reduction: Pushdown Automata recognizing context free languages with bounded stack

I am studying for an exam in automata theory and I am having trouble solving the following: Consider pushdown automata and context free languages. Show that the following decision problem is ...
1
vote
1answer
1k views

How to compute the consistency index in Analytic Hierarchy Process?

By studying AHP (Analytic Hierarchy Process), I have a question about RI. The (CI) is the consistency index. The RI value is fixed and is based on the number of criteria evaluated. $CR = CI / RI$ ...
0
votes
2answers
83 views

Making a decision

Like the title "Making a decision", I am standing for a problem. I've calculated two probabilities. $$P(\text{Match}) = 0.24$$ $$P(¬\text{Match}) = 0.76$$ Now I've to make a decision. Does ...
2
votes
0answers
102 views

Lower bound on uncertainty reduction

Let $T$ be a set of tuples such that each score tuple $s(t_i)$, $t_i \in T$ is uncertain (i.e., not known deterministically). The score $s(t_i)$ can be represented as a uniform probability density ...
3
votes
0answers
91 views

Inadmissibility of Simpson's rule

Let $B_t$, $t\ge0$ be a standard Brownian motion and suppose $0<x_1<x_2<\cdots<x_n<1$. Then the conditional expectation $$ \mathbb E\left(\int_0^1 B_t\,dt \,\middle\vert\, B_0, ...
0
votes
1answer
64 views

Lower Expectation

Let $X$ be, for simplicity, a finite set (with the discrete topology). Denote with $M(X)$ the set of probability measures on $X$ endowed with the weak topology. For $\mu\in M(X)$ and a (necessarily ...
1
vote
2answers
102 views

What is the most common decision making math model?

I have been told that there are psychological math model to make decision. I want to know what is it and how it work.
2
votes
1answer
199 views

Coin Game, Probability and Fairness

The following game is being played : Player $\mathrm{B}$ pays to Player $\mathrm{A}$ an amount $\mathrm{X}$ and throws a coin at most $20$ times. If at the toss $k\space (k \leq 20)$ tail is thrown, ...
0
votes
1answer
122 views

question related to Bayes' rule and Bays' risk.

Let $X_1, X_2, X_3, \ldots, X_n$ be a random sample for $N(e,1)$. Let the prior p.d.f. of $e$ be $N(0,\sigma^2)$ under the square error loss function $L(e,d)={(d-e)}^2$. Find the Bayes' decision rule ...
0
votes
1answer
97 views

Deducing probability of an event, when opponent's type is uncertain

Suppose, two players I and II, given a state space of three states$\{a,b,c\}$ with a common prior, $p(a) = p(b) =p(c) =1/3$, are endowed with two partitions of state space, $\mathscr{P}_\text{I} = ...
1
vote
2answers
813 views

Sum of two stopping times is a stopping time?

Let $\sigma$ and $\tau$ be two stopping times in $\mathscr{F}_t$ and let this filtration satisfy all the usual conditions. Question: Is $\sigma + \tau$ a stopping time? Attempt at a solution: I ...
1
vote
2answers
420 views

Mathematical Analysis of the Electoral College

Let us consider the electoral college voting system used to elect the American president. I have a few questions from the point of view of decision-making/gaming theory. My ultimate goal is to vote in ...
0
votes
1answer
94 views

How to formulate the probability of being correct?

Suppose we have the following Bayesian net (or a probabilistic graphical model): $L \rightarrow X \leftarrow F$, i.e. $P(L,X,F) = P(X|L,F)P(L)P(F)$ and all of these probabilities are known. Let ...
0
votes
1answer
77 views

Solution for assigning independent tasks to independent individuals

I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, ...
1
vote
2answers
84 views

Efficient method for testing membership

Suppose I have a finite set $S$ of real numbers, and let $F(S)$ be the set of real numbers which can be obtained by applying additions and multiplications to elements of $S$ and their additive and ...
1
vote
1answer
252 views

Maximum Likelihood optimal threshold

I have a decision (detection) problem trying to decide between symbols ${0,2}$. I have the two probability density functions: $$ f(z|s=0) = \begin{cases} 0.25z + 0.5, & -2\le\ z <0 \\ ...
4
votes
1answer
618 views

What is the relationship of $\mathcal{L}_1$ (total variation) distance to hypothesis testing?

Kullback-Leibler divergence (a.k.a. relative entropy) has a nice property in hypothesis testing: given some observed measurement $m\in \mathcal{Q}$, and two probability distributions $P_0$ and $P_1$ ...
0
votes
1answer
76 views

Best estimator when prior distribution is random

Maximum a posteriori estimator is a Bayes estimator under the 0-1 loss function and some given prior distribution. I was wondering how to give an estimation that is best in some sense if the prior ...