Questions tagged [decision-theory]

the mathematical study of strategies for optimal decision-making between options involving different risks or expectations of gain or loss depending on the outcome.

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19
votes
6answers
655 views

Experiments contradicting the expected utility model

This is a question I asked on the cognitive science beta which never got any answer there. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?)...
11
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2answers
869 views

Can the Machina Paradox be solved by expanding the choice set?

In another question, the Machina paradox is mentioned as a possible counterexample to the expected utility model: Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-...
7
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2answers
388 views

Definition of Absolute Risk Aversion

In its Wikipedia article, absolute risk aversion is defined as $ARA = -\frac{u''(c)}{u'(c)}$. However, I have alternatively seen absolute risk aversion defined as half the decrease in consumption ...
7
votes
2answers
3k views

Meaning of Additively Separable, Linear in X

Often I see both in micro and macro two common terminology : Additively separable. Linear in price or linear in probability. I understand exactly as they sound by looking at the functional form ...
16
votes
5answers
4k views

Topological concepts in economic theory

QUESTION: What are the major or systematic applications of post-1960s mathematics to microeconomics? For example, in the late 19th century, Fisher first used the mathematical ideas of Gibbs to ...
13
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3answers
2k views

Is there an economic analysis of the rationality of buying lottery tickets?

It's quite clear that the expected return on a lottery ticket is less than 1. However, I think it can still be argued that buying lottery tickets is still a economically rational decision by ...
1
vote
1answer
64 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 ...
5
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1answer
495 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 ...
3
votes
2answers
83 views

Exact definition of one-player Bayesian Correlated Equilibrium

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. ...
3
votes
1answer
4k views

Absolute vs Relative Risk Aversion

Are there results that says the monotonicity of one measure of risk aversion implies the monotonicity of the other measure? For example, Does constant relative risk aversion imply decreasing ...
3
votes
2answers
112 views

Properties of orders and preference relations

Suppose I have alternatives $A$, $B$, and $C$. If I have strict preferences, that means that for any $x,y \in \{A,B,C\}$ such that $x \ne y$, either $x \succ y$ or $y \succ x$. Assume transitivity, ...
3
votes
1answer
51 views

Example of information structure in a one-player Bayes Correlated Equilibrium

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
2
votes
0answers
42 views

$a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?

$\succsim$ is a continuous and local non-satiate weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (...
1
vote
1answer
49 views

How to derive formula for marginal probability of choosing nest in nested logit model?

I am trying to understand all the details of the nested logit and what confuses me is the formula for marginal probability of choosing the nest. In more details: the joint probability of individual n ...
1
vote
1answer
113 views

Set of Bayes Correlated Equilibria when complete information is not available

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
0
votes
1answer
49 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, ...