# Questions tagged [preferences]

Binary relations that reflect which states of the world an agent considers to be most desirable. Preferences are a fundamental ingredient in the axiomatic study of consumer choice decision theory.

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### Reconciling Continuity of Binary/Preference Relations with Continuity of Functions/Correspondences

There are various ways to express the concept of continuity of a binary relation, but one I've come across seems to imply the closed-graph property is sufficient. That is to say: For a nonempty set $X$...
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### Equivalence of two definitions of monotone preference

In MWG, the definition of weak preference is for all $x,y \in X$, $y>>x$ implies $y\succ x$ . But I have read some other articles that define weak preference as $y\geq x\implies y\succeq x$. ...
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### Determine Whether A Preference Relation Satisfies The Continuity Axiom - from Exercise 1.1 in Game Theory: Analysis of Conflict by Roger Myerson

I am self-studying game theory using Game Theory: Analysis of Conflict by Roger Myerson. Here is an exercise from the textbook. I tried it myself, but I am not sure if it is correct. I would really ...
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### y is weakly preferred over x if and only if x+y ≤ 4 defines a preference relation on {0,1,2,3} why is this incomplete?

y is weakly preferred over x if and only if x+y ≤ 4 defines a preference relation on {0,1,2,3}. True or False?. I can see why it's not transitive but I was told it was incomplete if we take 2 and 3. ...
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### Transitivity of Preferences paper

I am going through some of my old grad school notes, and in my microeconomics notes on transitive preferences, the teacher made a note of a behavioral economics result where when presented with two ...
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### Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?

For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$? Intuitively, this mean that we have two bundles, and ...
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### Lexicographic preference relation not continuous

I’m having trouble understanding why lexicographic preference relations aren’t continuous. I need inspiration on how this proof would work.
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### Properties of Consumer Preferences - Monotonicity

Was reviewing topics and I came across this question. I am confused because there is no reference to strict or weak monotonicity in this case. I first thought that monotonicity is violated b/c an ...
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### Quasiconvex and quasiconcave utility function

I saw that the model of the quasi-convex utility function is similar to the concave utility function and also the quasi-concave utility function is similar to the convex utility function. How can ...
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### Convexity preferences

What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
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### Reference for monotonicity: $x\geq y\implies x\succsim y$ and $x>y\implies x\succ y$

I've seen this definition for monotonicity many times on different papers and on this site: $x\geq y\implies x\succsim y$ and $x>>y\implies x\succ y$. However, what I read on MWG's ...
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### McKelvey-Schofield Chaos Theorem Without Agenda Setter

The McKelvey-Schofield Chaos Theorem states that in a multidimensional preference space, it is almost always possible to reverse engineer the implementation of your desired policy by constructing an ...
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### labor leisure model, quasilinear preferences

There is a quasilinear utility function $u= (1-t)wl - p(l)$, where $l$ is labor supply. I don't quite understand what happens, if the budget changes (due to $w$ or $t$) since it is quasilinear. Does ...
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### Sufficient conditions for connectedness of indifference sets of a preference relation defined on a compact and convex set only

Let $\succsim$ a complete, reflexive and transitive binary relation defined on $X$, a non-degenerated (i.e not identical to a singleton) convex compact subset of $\mathbb{R}^n_{++}$ (the set of n-...
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### Order relations and preferences using logic

I want to understand order relations using their underlying implication mechanics and what this means for certain results, specifically looking at preference relations. Using the logical rules of ...
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### Is it possible to get back the consumer’s utility function from their demand functions?

I am curious about if it’s possible to reverse the utility maximization process, i.e. given the consumer’s Marshallian demand functions, find their utility function. I was thinking of trying to find ...
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