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?)...
Martin Van der Linden's user avatar
17 votes
2 answers
7k views

What is the importance of Epstein-Zin preferences?

I've heard that there is a lot of work being done recently that applies Epstein-Zin preferences. The Wikipedia page doesn't seem to be very full. Why are Epstein-Zin preferences important? How does ...
jmbejara's user avatar
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16 votes
5 answers
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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 ...
user avatar
13 votes
4 answers
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 ...
dwjohnston's user avatar
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When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?

Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc. When $f$ is ...
EM23's user avatar
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12 votes
3 answers
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What are the recent advancements in building a unified theory of bounded rationality?

It seems that bounded rationality models focus on explaining a particular psychological bias, in a very specific way. In particular, its seems that the state of the art consensus is that one size does ...
user157623's user avatar
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11 votes
2 answers
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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-...
jmbejara's user avatar
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10 votes
3 answers
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Do a group of economic agents really act as if they are rational?

When questioning the rational choice hypothesis, I often get responses that are similar to the followings: "Individuals may sometimes make irrational decisions, but a large group of economic ...
user141240's user avatar
9 votes
2 answers
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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 ...
Frank Swanton's user avatar
9 votes
1 answer
3k views

Continuity Axiom in Expected Utility Theory

Take the following definition of continuity. The preference relation $\succsim$ over the space of lotteries $\mathcal L$ is continuous if for any $L,L',L''\in\mathcal L$, the sets $$S_1=\{\...
Herr K.'s user avatar
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9 votes
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The Savage sure thing principle and Subjective utility representation

I have tried reading and understanding Savage's proof of the subjective utility representation, it is too complicated. Is anyone aware of a shorter/more elegant proof of this? It is not a problem if ...
user157623's user avatar
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9 votes
1 answer
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Why is it possible to calibrate your subjective probabilities?

Humans tend to be overconfident in their predictions; when most people say that there's a 95% chance that something will happen, they're usually wrong far more than 5% of the time. Whereas what ought ...
Keshav Srinivasan's user avatar
8 votes
4 answers
207 views

What are different ways of specifying utility and decision making?

This question is related to this question about the Machina paradox and about the expected utility model. In this question, I'd like to know a little more about various or even competing ways of ...
jmbejara's user avatar
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8 votes
2 answers
185 views

Ordinally Separable Utility Representation

Let $X_i$ be a separable, compact, Banach space. Definition: A weak order $\succeq$ on $X=\prod_{i=1}^NX_i$ has an ordinally separable representation if there exists $u_i: X_i\rightarrow \mathbb{R}$ ...
Andrew McMillan's user avatar
8 votes
1 answer
803 views

Preference over lotteries without independence axiom

Suppose a set of $N$ outcomes can be ranked in the following order: $1\succ 2\succsim\cdots\succsim N$. Further, suppose a decision maker has preference over lotteries over these outcomes. Assume the ...
Herr K.'s user avatar
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8 votes
1 answer
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Which of Anscombe-Aumann's axioms imply the Sure-Thing principle?

Consider an Anscombe-Aumann setting, and assume that a preference relation satisfies all original Anscombe-Aumann's axioms (rationality, continuity, independence, and monotonicity). If we restrict ...
Oliv's user avatar
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8 votes
2 answers
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Moral Hazard with risk neutral agent

We have a principal-agent model with hidden actions in which the principal is risk averse and the agent is risk neutral; Assume also there are two levels of output, $x$ and $x'$ (with $x'>x$) and ...
night_owl89's user avatar
7 votes
6 answers
2k views

What are alternative measures of risk?

In finance, the variance of the returns of a security are used as a proxy for the associated risk of the security. I've seen some books include sentences like "if you take variance as a measure of ...
jmbejara's user avatar
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7 votes
2 answers
542 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 ...
jmbejara's user avatar
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7 votes
1 answer
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Lexicographic Preference Relation on the QxR

I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\...
Rororo's user avatar
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6 votes
3 answers
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What is the point of considering only pure strategies in a game? How could you restrict people from thinking about mixed strategy?

In an experimental setting, how could you effectively incentivize the subjects to not to adopt mixed strategy? I would like to re-emphasize that the question in concern is "how to prevent people ...
High GPA's user avatar
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6 votes
1 answer
450 views

Why stochastic dominance is "stochastic"?

I think the CDF is pretty much fixed, so the FOSD (first order stochastic dominance) is pretty much non-stochastic. Why does it have a "stochastic" in its name?
High GPA's user avatar
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6 votes
1 answer
194 views

Consequences of hyperbolic discounting

In reading the Wikipedia article about hyperbolic discounting, I read that it says that hyperbolic discounting created strange consequences: But note, the time inconsistency of this behavior has ...
jmbejara's user avatar
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6 votes
1 answer
105 views

Is there a school of thought or concept that acknowledges that people aren't rational actors when it comes to economic decisions?

People are subject to all sorts of cognitive biases. For example: Advertising works, and not just by making people aware of a product, but by appealing to emotional quirks. People are subject to ...
dwjohnston's user avatar
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6 votes
1 answer
588 views

Why is the Marginal Utility of losses diminishing in Prospect Theory?

This is Kahneman's value-plot on prospect theory: QUESTION: Why is the Marginal Utility of losses deminishing? CONTEXT: I fully understand that the Marginal Utility of gains deminishes: 100 dollar ...
GambitSquared's user avatar
6 votes
1 answer
258 views

GARP and SARP assumed mononticity?

Monotonicity means the decision maker prefer more goods than less. It is not mentioned in textbook that SARP and GARP preasumed monotonicity, implicitly. GARP: if $a$ is indirectly revealed preferred ...
High GPA's user avatar
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6 votes
1 answer
688 views

What is the advantage and disadvantage of fiscal illusion policy in terms for the financial market?

What is the advantage and disadvantage of fiscal illusion policy for the financial market? Fiscal illusion suggests that when government revenues are not completely transparent or are not fully ...
Victor's user avatar
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1 answer
583 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 ...
Kenneth Chen's user avatar
5 votes
2 answers
123 views

Information structure for complete information

Model A decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. $\mathcal{Y}$ is a finite set. The state of the world is a random ...
Star's user avatar
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5 votes
1 answer
102 views

Interpreting the ratio of two variances in a Bayesian decision problem

Given a normal prior with mean $\mu_0$ and variance $\sigma_0^2$, and a normal likelihood with known variance $\sigma^2$, the Bayesian posterior, after observing $n$ iid signals $x_1,\dots,x_n$, is ...
Herr K.'s user avatar
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5 votes
1 answer
200 views

Portfolio choice of a risk lover

Take the standard portfolio choice problem as presented in MWG (p.188-189), but with a risk loving decision maker: with initial wealth $w$ invests an amount $\alpha$ in a risky asset with a random ...
Herr K.'s user avatar
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5 votes
1 answer
273 views

Fantasy football

I have an idea for a fantasy football experiment looking at three different areas of the draft. These three areas are the position of each pick and how often and what value are trades. I have dug ...
user4318524's user avatar
5 votes
0 answers
47 views

Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
cfp's user avatar
  • 252
5 votes
0 answers
137 views

Certainty equivalence when the utility is semi-continuous instead of continuous

Let $U:\mathbb R^2\to\mathbb R$ be a utility function. If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,...
High GPA's user avatar
  • 1,906
5 votes
0 answers
133 views

Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
High GPA's user avatar
  • 1,906
4 votes
3 answers
2k views

What are good mathematics books to learn decision theory?

I am looking for a set of mathematics books to understand proofs in decision theory. Examples would be proofs of utility representations and social choice (im-)possibility results. I found many ...
HRSE's user avatar
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4 votes
1 answer
282 views

What is the difference between Impression Management and Signaling Theory?

I'm interested in theories on how organisations shape their stakeholders' (especially consumers' and investors') perceptions and decisions. I read about Impression Management and Signaling Theory. ...
TiTo's user avatar
  • 143
4 votes
1 answer
272 views

Does Debreu's representation theorem of ordinal utility require Hausdorff topology?

By Debreu's theorem of ordinal utility, any continuous weak order on $X$ is represented with a continuous utility function, if $X$ is a second countable or connected separable topological space. My ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
104 views

Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU? To my knowledge, most utility functions under risk and ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
83 views

What is the economic intuition of prudence in the static case?

How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)? I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
ju_pi_car's user avatar
4 votes
1 answer
73 views

Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
Beerus's user avatar
  • 325
4 votes
1 answer
77 views

In revealed preference (RP), is any two points $x,y$ related by the indirect revealed preference relation?

Let $X$ be the closed compact convex set of alternative and $B$ be a closed compact convex subset of $X$. $C$ is defined on all closed compact convex set $B\subseteq X$. $X$ is ordered by a strictly ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
328 views

Blackwell order of information structures

Consider a model 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 $\mathcal{V}$. ...
Star's user avatar
  • 436
4 votes
2 answers
469 views

Does the Prospect Theory value curve change according to reference wealth size?

After reading "Thinking Fast and Slow" and half a day of internet search on this topic I resort now to asking this question here. Prospect Theory seems to only attribute value to changes in wealth. ...
jasper's user avatar
  • 41
4 votes
1 answer
273 views

Markov decision processes, contractions and value iteration

I am reviewing Markov decision processes (MDP) and there is something I am missing with respect to the contraction argument. I am pretty sure it is a silly mistake somewhere (maybe computational), but ...
Martin Van der Linden's user avatar
4 votes
0 answers
86 views

Who were the first economists arguing that utility maximization is the core of rationality and economic behavior?

I am looking for the first economists arguing that maximizing utility function is the iff condition of rational behavior. I've learned that neoclassical economics is founded on this argument. Is this ...
High GPA's user avatar
  • 1,906
4 votes
0 answers
177 views

Social Choice: from Independence axiom to Mixture symmetry axiom

Harsanyi's Utilitarian theorems' has been criticized by Diamond Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utilities and others that, it is the morally unacceptable for ...
Bob's user avatar
  • 263
3 votes
5 answers
8k views

Violation of completeness axiom (simple everyday examples)

Simple everyday examples of violations of transitivity are not difficult to come up with, but I'm having trouble thinking of some for the completeness axiom. One possible formulation of the ...
user avatar
3 votes
1 answer
392 views

Is First Order Stochastic Dominance (FOSD) relation convex?

A convex relation is that $x\succeq y$ implies $\alpha x+(1-\alpha)y\succeq y$. Let $>_{FOSD}$ be $\succ$, is the FOSD convex? Intuitively it seems convex.
High GPA's user avatar
  • 1,906
3 votes
1 answer
114 views

How to determine if people behave optimally with a generic utility function?

I have a some real-world data and a real-world choice for which I know the optimum solution is something like $y^* = u(x)$, where $u(.)$ is some utility function. I have data on $y$ and $x$, so if I ...
aintgeorge's user avatar