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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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Example of a rational and continuous preference relation that does not admit a utility representation

It is well-known that a rational, continuous and monotone preference relation $\succeq$ defined on $\mathbb{R}^L$ admits a utility representation. I would like to understand why monotonicity is ...
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Textbooks addressing MDP's in microeconomics/game theory/decision theory?

I have learned about the MDP formalism in the context of machine learning. I know that micro theorists also study MDP's, and agent behaviour in this context (both single and multi-agent I think). I ...
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reference request: models of how racism or sexism affects decision making

My background is more in statistics and applied math, so I am not familiar with the breadth of decision making models from economics. However, I am working on a project that involves decision making ...
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27 views

Does Pascal's Wager fail archimedean property?

I assume most people have heard of Pascal's Wager, in case you have not: https://en.wikipedia.org/wiki/Pascal%27s_Wager By the Stanford encyclopedia of philosphy: "We have a decision under risk,...
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Question about the “No Dictator” Criterion in Arrow's Impossibility Theorem

I have a question about Arrow's impossibility theorem. I'm not sure I understand exactly what is meant by the "no dictator" criterion. Does the presence of a "dictator" mean that across all possible ...
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1answer
268 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?
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The connection between risk and the quality of investment decision

Is there any psychological model that suggests that for optimum quality of investment decision, there has to be some risk involved?
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30 views

Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
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39 views

Afriat's number

I discovered the Afriat's theorem on the possible rationalization of a given data set of demand observations and would like to ask for your help in understanding how to compute Afriat numbers in ...
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162 views

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 $\...
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Beta delta Agent - Consumption decision

I’m struggling with a problem regarding the beta delta agent. Can someone give me a hint how I can come up with the levels of utility? Thanks in advance!
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What do you call a system in which the payer is not the decision maker?

Is there a name for a system in which the person/entity who makes the buying decision is not the same as the person/entity who pays? Specific examples of this might be situations which arise in ...
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Philosophy books for decision theory and economics idea

I have learned economics so far, the most astonishing economics' thing is its though which is talkable and visually in the real world or the abstract world that is worth researching and talking. What ...
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158 views

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 ...
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2answers
160 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. ...
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1answer
198 views

Why is the Marginal Utility of losses deminishing 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 ...
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41 views

Measuring Subjective Beliefs

I am starting on a research project that requires the measurement of subjective beliefs of subjects around uncertainty. Since I'm new in this field I'm looking for references that can help me get ...
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Has any person ever actually planned his or her consumption according to Modigliani’s LCH?

https://en.wikipedia.org/wiki/Life-cycle_hypothesis?wprov=sfti1 It seems self-evident to me that nobody on Earth actually does this. Real people are short-sighted, undisciplined, and lack the ...
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112 views

What are some non-von-Neumann-Morgenstern preferences used in economics?

Von-Neumann Morgenstern preferences are preferences over lotteries that can be represented as the expectation of a "deterministic" utility function over outcomes. "non-von-Neumann-Morgenstern" ...
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vNM Expected Utility Theorem Proof

I have been asked by my professor for Decisions Theory to refer to David M. Kreps' Notes on Theory of Choice for the proof of the vNM theorem of expected utility. Before the proof of the theorem ...
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Was there resistance, historically, to the idea that human behavior deviates from rational decision making theory?

I have edited this question considerably to narrow the focus. A recent New York Times article was published on the Nobel Prize for Economics. The article discusses that Nobel laureate Richard Thaler ...
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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 ...
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1answer
104 views

What does non degeneracy mean for a preference?

I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior). The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$". So can you explain ...
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Is the dictator game studied by game theory or by decision theory?

Is the dictator game/dilemma studied by game theory or by decision theory? I'm not sure because of the lack of other interactive agents.
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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 ...
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Kahneman and Tversky Decision experiments contradict Neumann-Morgensterns utility theory [duplicate]

I want to know the reason why Kahneman and Tversky Decision experiments contradict Neumann-Morgensterns utility theory. Could anyone please ellaborate this to me? Thanks.
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Additive multiattribute nonlinear utility functions

I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form: $u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \...
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153 views

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 ...
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62 views

What factors affect the temporal discount rate individuals apply in decision making?

Discount rate is rate at which actors will value something that occurs in the future at less than its value now. A simple hypothetical test that would determine this would be: 'Would you rather ...
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Is maximal utility conditional on information linear in convex combinations of priors?

This is related to a Mathematica question here - https://math.stackexchange.com/q/1952779/374929 Is a (maximal expected utility) function of the form $U(\mu, X) \equiv \int_\Theta \int_\mathcal{X} \...
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1answer
82 views

Trade-off between determenistic and random alternatives in a one-shot game

I wonder how to analyze the following problem. Suppose we play a one-shot game. We have two options. We can either get $x$ dollars or win $y$ dollars with probability 50% (or, probably, win nothing ...
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1answer
103 views

Decision to make one side of a multisided platform the subsidy side

I'm reading Matchmakers: The New Economics of Multisided Platforms by economists David S. Evans and Richard Schmalensee. They describe how businesses often make a rational choice to allow one side of ...
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Has anyone studied how people's indifference curves can change?

I'm wondering if anyone has looked at how people's indifference curves can change, whether systematically due to experimental manipulations, or if they just vary due to noise. I thought about this ...
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What models exist that explain which people emigrate to another country?

I'm looking for papers about this, or if there's a pretty standard model across many papers, then maybe just a rundown of the model. I'd like to use the model in an econometric analysis. For example, ...
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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 ...
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417 views

Representing these lexicographic preferences by non-continuous utility function?

I have the following preferences and I am wondering whether I could represent them by a utility function: $R_1 \succ R_2$ <-> $R_1\leq Q$ and $R_2 > Q$, $R_1 \succ R_2$ <-> $R_1 \leq Q$ and ...
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202 views

Question about Gilboa and Schmeidler “A Maxmin Expected Utility With Non-unique Prior” 1989

I have a question on the proof of lemma 3.3: Let $g\in L_0$ satisfy $u \circ g = b$, $z\in Y$ satisfy $J(z)=0$ where $J$ satisfy lemma 3.2, and let $f=\alpha g + (1-\alpha)z$. Then $u\circ f = \alpha ...
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46 views

Best terminology for “inverse” preferences

This might be related to : Symmetric and asymmetric preferences. In your experience, what is the best terminology to denote a pair of preference relations $(R,R')$ over some set of alternatives $A$ ...
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506 views

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 ...
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156 views

List of behavioral economists [closed]

Even though there is a massive literature on behavioral economics, i couldn't find anywhere a list of economist that focus on that discipline. Since i am interested in environmental economics, i ...
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93 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, ...
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1answer
224 views

Decision Theory Question: Existence and uniqueness of the certainty equivalent of p

Let $X = (x_*,x^*)$ be an interval in the real line and denote by $\Delta(X)$ the set of simple probability distributions on $X$. Consider a preference relation $\succcurlyeq$ on $\Delta(X)$ that ...
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2answers
484 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 ...
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383 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 ...
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How does the maximin and lexical maximin rules work in these two decision tables?

sorry to bother you guys but I've been pulling my hair out over this one. I would like to know why the maximin rule excludes act A1 in the following decision table - why does this happen, given that ...
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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=\{\...
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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 ...
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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 ...
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509 views

Intertemporal consumption question

This question is driving me nuts. Suppose, an individual lives for two periods. In each period she consumes only one good,which is rice. In period 2, she can costlessly produce 1 unit of rice, but ...
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How much was it going to cost to pay Bombardier a premium to restart production of Mark I trains? [closed]

I read many web pages discussing the future plans of the Scarborough RT and the cost of plans they were planning to do but not the cost of the premium they decided not to carry on with. Without ...