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11 votes
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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 ...
Ubiquitous's user avatar
9 votes
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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 ...
Bayesian's user avatar
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8 votes
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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 ...
Alecos Papadopoulos's user avatar
8 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. *$...
123's user avatar
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8 votes
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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 ...
201p's user avatar
  • 956
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 (...
Michael Greinecker's user avatar
7 votes
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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, $F$ ...
Herr K.'s user avatar
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7 votes
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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 ...
Michael Greinecker's user avatar
7 votes
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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 ...
Michael Greinecker's user avatar
6 votes
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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-\...
Lorenzo Castagno's user avatar
6 votes
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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 ...
Bertrand's user avatar
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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 ...
Michael Greinecker's user avatar
5 votes

Lexicographic Preference Relation on the QxR

Note first that for each nontrivial (more than one point) compact interval $I$, there exists a strictly increasing function from $\mathbb{R}$ to $I$. Let $\langle q_1,q_2, q_3,\ldots\rangle$ be an ...
Michael Greinecker's user avatar
5 votes

Experiments contradicting the expected utility model

Picking up my comment under this answer. One striking issue relevant to decisions not captured by expected utility is the framing effect discussed by Tversky and Kahneman (1981) and others. In their ...
Bayesian's user avatar
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5 votes
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Can mixed strategies actually predict behaviour of rational actors in non-constant sum games?

There is a series of papers that address precisely this question. The most famous ones are probably Walker and Wooders (2001) and Chiappori, Levitt, and Groseclose (2002) that deal with penalty kicks ...
brunosalcedo's user avatar
5 votes

What is the point of considering only pure strategies in a game? How could you restrict people from thinking about mixed strategy?

The real-life question is "how do you persuade people to use mixed strategies"? To stick with your example, Consider a person that has to make a binary choice $(H, T)$, and, after ...
Alecos Papadopoulos's user avatar
5 votes

Question about Social Welfare Function and Social Profile

In its most general formulation, a social welfare function is just a utility function representing the preferences of "society as a whole" (or the preferences of a hypothetical "...
Marcus Pivato's user avatar
5 votes

Can any three of the four vNM axioms (of expected utility theory) be satisfied without satisfying the fourth?

(1) Satisfying completeness, independence, and continuity but not transitivity: Take two outcomes, $\{0,1\}$, and the associated lottery space $[0,1]$. Consider the preference relation $\succsim$ ...
axelniemeyer's user avatar
5 votes

Do a group of economic agents really act as if they are rational?

Can you explain the rationale behind the above statement in further details? This is an example of an emergent property or sometimes called just emergence. Emergence in layman's terms denotes ...
1muflon1's user avatar
  • 57k
5 votes

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

There is a whole literature on revealed preference analysis that looks at the testable implications on choice (consumption) data without imposing any functional form on the utility function. Is this ...
tdm's user avatar
  • 12.4k
4 votes

Violation of completeness axiom (simple everyday examples)

There is a problem in how you translate completeness into behavior. Let $R$ be any binary relation, representing preferences, on a set $X$ of alternatives and $A\subseteq X$ be a nonempty set of ...
Michael Greinecker's user avatar
4 votes

Experiments contradicting the expected utility model

Let me mention another quite well-known one: The calibration theorem by Rabin (2000) and Rabin and Thaler (2002). The idea is that over small stakes individuals must be essentially risk-averse, but in ...
Bayesian's user avatar
  • 5,291
4 votes

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

The value function used in Kahneman's prospect theory (which your plot shows) is supposed to capture empirically observed behavior of people's attitudes towards gains/losses as well as to risks in ...
Herr K.'s user avatar
  • 15.4k
4 votes

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

The von Neumann-Morgenstern (vNM) utility function takes the form \begin{equation} U(p,x)=\sum_{i=1}^np_iu(x_i) \end{equation} where $x=(x_1,\dots,x_n)$ with $x_i$ being the (monetary) payoff ...
Herr K.'s user avatar
  • 15.4k
4 votes
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Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

I think that you should proceed by contradiction assume D is continuous, but $\succsim$ is not, then for a bundle either the more preferred than or the less preferred than sets are not closed. Choose ...
Regio's user avatar
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4 votes
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A weaker definition of local non-satiation can also imply indifference "curve"

(2) does not imply (1). Consider a utility function with "circular indifference curves", e.g. $u(x,y)=-(x-1)^2-(y-1)^2$. At the bliss point $(1,1)$, the function satisfies (2) but violates (1). (2) ...
Herr K.'s user avatar
  • 15.4k
4 votes
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Boots' Theory by Pratchett

Rampini elaborates on your idea (and also the Pratchett quote) in his AER article "Financing Durable Assets". See the abstract: This paper studies how the durability of assets affects ...
Bayesian's user avatar
  • 5,291
4 votes
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What is the definition of: 'commodity space'?

Yes, a commodity space is the set of all possible commodity bundles. The simplest Micro 101 example is typically the nonnegative quadrant of $\mathbb{R}^2$, but in general equilibrium theory it is ...
VARulle's user avatar
  • 6,994
4 votes

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 prevent the players from adopting a mixed strategy? I don't think you can. Restricting access to mixed strategies is essentially banning the use of any ...
Herr K.'s user avatar
  • 15.4k

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