Questions tagged [choice-theory]

a conglomerate of models and results concerning the aggregation of individual choices into collective choices

Filter by
Sorted by
Tagged with
3
votes
2answers
48 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 $\mathcal{V}$. ...
1
vote
1answer
33 views

Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is ...
1
vote
1answer
45 views

Risk neutrality in single-agent choice problem under uncertainity

Consider the following static single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{V})$. ...
1
vote
1answer
63 views

Sen's property $\alpha$ holds when limited attention in choice?

Consider the limited attention choice framework by Matejka and McKay (2015). This framework can give rise to consideration sets, as roughly summarised below. Consideration sets in the limited ...
1
vote
1answer
59 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 ...
1
vote
1answer
72 views

Boots' Theory by Pratchett

Consider the following quote from the book, $\textit{Men at Arms}$ by Terry Pratchett. “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money. ...
0
votes
2answers
68 views

The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
4
votes
0answers
36 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 ...
1
vote
0answers
55 views

Archimedean but not mixture continuous

In the context of preferences on a set of lotteries on a finite set $X$, what is an example of a preference that is independent, Archimedean but not mixture continuous? I know the mixture continuous ...
0
votes
1answer
39 views

What does irrationality mean under the notion of revealed preferences? An example with terrorism.

I am currently studying for an economics of conflict exam and one of the potential questions is likely to be in the vein of "Are Terrorists Rational - Discuss". However how would rationality be ...
3
votes
2answers
152 views

a risk lover agent preferences and the preference of risk natural agent may be the same

Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ ...
2
votes
1answer
256 views

Choice correspondence notation

My question is about the following notation: I have noticed in several places (for example here (page 15) and here (page 1)) that different authors use different notations for choice correspondences....
6
votes
1answer
219 views

Envelope theorem for discrete choice sets?

If we have a function $$f(x)=\max_yg(x,y)$$ Then we can find the derivative $d/dx \ f(x)$ by realizing that $$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$ because of the first order ...
2
votes
1answer
269 views

What is the economic incentive to cheat? How does an experiment capture exogenous deviations?

In my undergraduate career an economic experiment was conducted on my class: one class was the control two classes were the experimental (I was in an experimental class) The basic premise was a ...
1
vote
1answer
52 views

Is this proof correct?

i'm new at this, so i´m really sorry sorry if i do something wrong. The problem is this: A choice function satisfies condition α if whenever $x = C(A)$ and $x ∈ B ⊂ A$, it follows that $x = C(B)$ as ...
3
votes
0answers
341 views

Choice rule and path independence

Question: A choice rule $C$ satisfies path independence if for all $A, B \in 2^X \setminus \emptyset$, $C(A \cup B) = C(C(A) \cup C(B))$. Prove that if $C$ is nonempty and rationalizable, then $C$ ...
1
vote
1answer
39 views

Vocabulary/Name for Utility of a Set of Choices

I am trying to find if there is some litterature or definition of the concept of the Utility of a set of choices. My google searches return nothing, and I expect it is because I do not know the right ...
1
vote
1answer
70 views

What is one dimensional, ordered type?

I am reading papers about moral hazard. What is one dimensional, ordered type $\theta\in\Theta$? What is one dimensional, not ordered type $\theta\in\Theta$? Could you please give an example? ...
2
votes
1answer
271 views

Inc Linear Transformation of Bernoulli Utility

According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation. What is the significance of this proposition? The part I ...
1
vote
1answer
74 views

Consequentialist View of Risk

In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker. From philosophical view, ...
0
votes
1answer
244 views

Troubleshooting Utility Maximization with the Lagrange Method

I'm trying to solve a utility maximization problem through the Lagrange method. The utility function is something like $u(x,y)=x+B(y-a)$. However, I'm running into problems as x and y do not come up ...
2
votes
2answers
6k views

Relation between linear utility function and U=max{x,y}

I'm studying general equilibrium theory, and in the study guide I came across a utility function of the type $U=\max\{x,y\}$, which I'm not that familiar with. I study mainly from two books: ...
0
votes
2answers
660 views

Whom would you consider to be the father of rational choice theory? [closed]

Whom would you consider to be the father of rational choice theory? My suggestions that would qualify for major publications: Arrow (1959), Economica Homans (1961) Becker (1976) Sugden (1991), ...
2
votes
1answer
207 views

Consumer demand: a function of present endowment?

I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the ...
2
votes
2answers
126 views

Can there be sensible choice behavior that violates the Weak Axiom of Revealed Preference?

Following the notation of Mas-Collel, Whinston, and Green, consider a family of budget sets $\mathcal{B}=\{\{x,y\},\{x,y,z\}\}$. To make the example concrete, let's let $x$ be a book $y$ be a left ...
1
vote
2answers
663 views

My Challenge in Econ 101 explanation of Marginal Benefit = Marginal Cost

In Econ 101 textbooks, there are lots of examples and emphasis on marginal analysis leading to the greatest equation of all, $MB=MC$. My challenge is the following and wonder if anyone had a similar ...
1
vote
1answer
76 views

Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$

This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set. Some books appeal ...
1
vote
1answer
1k views

Why is Price Vector Orthogonal to Vector connecting two bundles on Budget Hyperplane

Here is my revised version/understanding why price vector is orthogonal to any vector from a bundle on the budget hyperplane to another bundle on the hyperplane: (see below for original question) ...
1
vote
1answer
384 views

Continuous Preference Relation Imply Continuous Utility Fn Existence

I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function. First, the authors show $u(.)$ is continuous by using the ...
3
votes
1answer
3k views

(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets

[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
4
votes
2answers
864 views

Continuous rational and monotone preference relation implies $x\succsim0$?

I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks Show a monotone continuous complete preorder on $\mathbb{R^L_+}$ has $y\geq x\rightarrow y\succsim ...
6
votes
3answers
1k views

What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
5
votes
3answers
327 views

The 'Economic Man' (Reference Request)

We are writing a paper about the 'economic man.' By this, we mean that the choices he makes epitomize a rational economic thinker. However, we also acknowledge the fact that there are other, non-...
1
vote
1answer
295 views

performance as utility function / price?

I am trying to define a 'model' for the perceived performance of a product based on this definition: Presumably, customers take both price and quality into account as they form an overall ...
9
votes
5answers
1k views

Are terrorists rational?

Terrorism in general, and suicidal terrorism in particular, is popularly seen as “irrational,” but many economists and political scientists argue otherwise. This quote is from Terrorism: The ...
6
votes
1answer
481 views

Prove that a continuous $\succsim$ is quasilinear

This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b Let $\succsim$ be a strictly monotone, continuous, and rational preference relation on $(-\...
7
votes
2answers
6k views

What is the difference between “Social Choice Theory”, “Public Choice Theory”, and "Collective decision-making?

I need to know the difference between Social Choice, Public Choice and collective decision-making. Also, Is public choice, social choice the same as collective choice? Thank you
1
vote
1answer
37 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 ...
2
votes
2answers
1k views

Weak axiom of revealed preference and choice coherence - how to show they are equivalent

$B$ and $B'$ are elements of the family of subsets of $X$ WARP For every pair $x,y \in B \cap B' $ and if $x \in c(B)$ , then if $y \in c(B'), x$ must $\in c(B').$ Choice Coherence For very pair $x,...
3
votes
0answers
126 views

Proof of Proposition 1.4 from Microfoundations I by Kreps

Regardless of the size of X (set of all possible objects), if a preference relation which is complete and transitive is defined on it, then the corresponding choice function generated by it will ...
7
votes
1answer
1k views

Condorcet's paradox: Is the majority rule transitive?

From this wikipedia link I would say that the majority rule is not transitive. Also I'm not sure I understand exactly what is transitivity in this situation... With a usual preference relation $x\...
5
votes
3answers
2k views

intertemporal utility function usage : calculating consumption

I have encountered this a lot in my exams and can not seem to understand how to use these functions here is an easy exemple : A consumer who will only live 2 periods receives 1000€ in the first ...
3
votes
1answer
259 views

Microeconomic foundation of discrete choice model

(1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function? A consumer $i$ maximizes a utility $u_{ij}$ in choosing one of J ...
1
vote
2answers
1k views

What is an example of a choice which is not necessitated by scarcity?

I am first year economics student and for the past month we have had it constantly drilled into us that all choices have an opportunity cost and thus they are all necessitated by scarcity. Thus when I ...