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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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?)...
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-...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $\mathcal{V}$. ...
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 ...
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, ...
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{... 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 (... 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 ... 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{...
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, ...