13
votes
Accepted
Topological concepts in economic theory
I strongly suspect that an emerging important area for applications of measure theory will be in approximate dynamic programming techniques. Approximate dynamic programming (aka "reinforcement ...
- 1,048
12
votes
Experiments contradicting the expected utility model
this paper http://else.econ.ucl.ac.uk/papers/uploaded/243.pdf (Choi 2007) has a nice state of the art experiment that deals with rationality and expected utility is a special case of it. In general ...
- 1,393
12
votes
What is the importance of Epstein-Zin preferences?
This is only a quick answer, unfortunately. The key intuitive insight for Epstein-Zin is that they separate two distinct properties of preferences: risk aversion ("I'd prefer less uncertainty to more ...
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12
votes
Accepted
Continuity Axiom in Expected Utility Theory
It is.
Prior to continuity, which is a property of the preference relation, the preference relation $\succsim$ itself has been defined to be a binary relation that is characterized by transitivity, ...
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11
votes
Accepted
What is the importance of Epstein-Zin preferences?
I think CompEcon covered most of the points that I was going to mention. Just a few last thoughts:
1) Why are Epstein-Zin preferences important?
The preferences are important because they allow you ...
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10
votes
Is there an economic analysis of the rationality of buying lottery tickets?
There are definitely economic justifications for playing the lottery, even if all (I hope) players understand that it is unlikely to pay off.
One such justification is that what you actually buy when ...
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10
votes
Accepted
Why stochastic dominance is "stochastic"?
In the below figure, CDF $F(\cdot)$ is first-order stochastically dominated by $G(\cdot)$. But $X_1$ and $X_2$ fall within the support of both distributions. So it would be possible to draw $X_1$ from ...
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9
votes
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Preference over lotteries without independence axiom
No, not necessarily. Without the independence axiom (or something else to replace it) there is not much you can infer about preferences over (non-degenerate) lotteries from knowing preferences over ...
- 5,167
9
votes
Experiments contradicting the expected utility model
Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-Colell, Whinston and Green's Microeconomic Theory.
A person prefers a trip to Paris to watching a television ...
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8
votes
Topological concepts in economic theory
This was too long for comment. "Post 1960" seems an arbitrary and very high bar for an applied field, including micro theory. Most of the topics you name would not be considered contemporary ...
- 2,559
8
votes
Consequences of hyperbolic discounting
As often with models embodying some form of "irrationality" (whatever that means), HD does a great job at matching a whole lot of behaviors, but leaves room for rather annoying Dutch Book situations (...
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8
votes
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Independence axiom of lottery when $\alpha \ge 1$
To understand why $\alpha$ must be constrained in $(0,1)$, one has to contemplate the meaning of the expression
$$\alpha L$$
when $L$ is a "lottery". How is a lottery denoted mathematically? Authors ...
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8
votes
Accepted
Which of Anscombe-Aumann's axioms imply the Sure-Thing principle?
As a first remark: the Anscombe-Aumann axioms, in particular Independence, are defined over acts taking the state space to a linear space (generally simple lotteries over consumption objects). Even ...
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8
votes
What is the point of considering only pure strategies in a game? How could you restrict people from thinking about mixed strategy?
If in equilibrium, a player "chooses a mixed strategy" that plays $H$ and $T$ with positive probability, $H$, and $T$ must be both optimal choices. It is a standard result that for a (...
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7
votes
Is there an economic analysis of the rationality of buying lottery tickets?
I want to add some other justifications for buying lottery tickets:
general risk-seeking behavior (which is probably pretty rare)
risk-seeking when it comes to low monetary values (Cumulative ...
- 1,682
7
votes
Accepted
What are good mathematics books to learn decision theory?
I do not know about social choice, but for utility representations I think the two most cited books are "Convex analysis" by Rockafellar and "Infinite Dimensional Analysis: A Hitchhiker's Guide" by ...
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7
votes
Meaning of Additively Separable, Linear in X
A utility function is additively separable if it can be written as:
$U(x,y) = u(x) + v(y)$
Examples:
*$U(x,y) =ax + by$ is additively separable by inspection.
*$U(x,y) = ax + bx2 + cy$ is also.
*$...
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7
votes
Accepted
Meaning of Additively Separable, Linear in X
A function is additively separable in its arguments if it has the form
$$f(x,y) = g(x) + h(y)$$
This means that the cross partials are zero, and so there is no "cross" effect of the one argument ...
- 31.8k
7
votes
Accepted
Is First Order Stochastic Dominance (FOSD) relation convex?
The first order stochastic dominance relation is convex.
An easy way to prove this is to use the property that a cdf $F$ FOSD another cdf $G$ if and only if $F(x)\le G(x)$ for all $x$. That is, $F$ ...
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7
votes
Accepted
What is the difference between Impression Management and Signaling Theory?
I don't believe those two terms are used in the same spheres.
To me, an economic theorist, signaling plays a role in models with asymmetric information when the informed party moves first and the ...
- 5,090
6
votes
What are different ways of specifying utility and decision making?
I'm somewhat surprised that no one has linked to this paper: Backus, Routledge, and Zin (2004) Exotic Preferences for Macroeconomists (this version has some fixed typos, vs the NBER print).
Their ...
- 1,048
6
votes
Can the Machina Paradox be solved by expanding the choice set?
No, I would not say that this resolves the Machina paradox, because it is exactly the same as the Machina paradox: the paradox does indeed require from you to look at the three possible outcomes. The ...
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6
votes
What are different ways of specifying utility and decision making?
This won't get at individual choice, but how about evolutionary approaches? Perhaps this isn't what you are looking for, but one way to model decisions is to wander from the rational paradigm entirely....
- 2,167
6
votes
When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?
After the exchange with the OP in my other answer, let's work a bit with his approach.
We have a discrete random variable $X$ with finite support, $X = \{x_1,...,x_k\}$, and probability mass ...
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6
votes
Accepted
If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?
It's well known that if $\succsim$ satisfies independence, then it is also convex.
Since $\succsim$ satisfies independence,
$L\succsim L^{'} \iff \alpha L+(1-\alpha)L^{''}\succsim \alpha L^{'}+(1-\...
- 278
6
votes
Accepted
Ordinally Separable Utility Representation
Here is the sketch of a proof. All we need is that every continuous weak order on each $X_i$ admits a continuous utility representation. One sufficient condition is that each $X_i$ is a connected ...
- 9,705
6
votes
Accepted
Do a group of economic agents really act as if they are rational?
The literature is full of examples in which either
individual rationality leads to aggregate rationality
individual rationality does not yield aggregate rationality (when public goods or ...
- 2,552
6
votes
Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?
Many people accept the axiomatizations of expected utility as normatively appealing, especially in contexts of pure risk. For people with this view, rational decision-makers should behave in ...
- 9,705
6
votes
Accepted
Does Debreu's representation theorem of ordinal utility require Hausdorff topology?
No. However, the problem can be reduced to representing preferences on a Hausdorff space. Instead of trying to represent a complete preorder on a set, one can try to represent linear orders on the ...
- 9,705
5
votes
Topological concepts in economic theory
Measure theory is widely used in the problem of fair division (aka "cake-cutting"). See the many papers about fairness in economics journals.
For a particular example, see Tatsuro Ichiishi and Adam ...
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