# 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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### How could define the certainty equivalent in a Bayesian Persuasion model?

For once again I will start describing the Kamenica and Gentzkow Bayesian persuasion model. Suppose that $\Theta$ is a finite set of states and $\theta$ is the element of the state set. To simplify ...
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### Non-nullity assumption in vNM theorem of cardinal utility

The vNM theorem suggests that weak-ordering, continuity, and independence is equivalent to the existence of expected utility, unique up to an affine transformation. In Savage's axioms of expected ...
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### Debreu's cardinal representation theorem for finite outcome set

Suppose there are three dimensions. $x,y,z\in X^3$. Independent: $z_ix\succsim z_iy\iff z'_ix\succsim z'_iy$. When $X$ is connected topological space, Debreu proved that weak order, independent, and ...
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1 vote
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### Kohlberg-Mertens theorem

I am trying to understand the Kohlberg-Mertens theorem. Here is the context and the theorem. We fix $N$ a set of players and $S_i$ the finite set of actions of each players with $\lvert S_i\rvert =m_i$...
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### Independence Axiom and Expected Utility Theorem Proof

In my micro class we covered the proof of the existence of a Von Neumann–Morgenstern utility representation of preferences $\succeq$ over a set of lotteries $\Delta(Z)$ - where $Z$ is some finite ...
65 views

### 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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1 vote
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### Trying to find a proof for Strong Axiom of Revealed Preference with general choice set

Note this is question is not about consumer demand with price and income data. This is a question about general choice theory. For reference, see: https://www.jstor.org/stable/2550390 See Debreu's ...
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### Equivalence of two definitions of revealed preference

Given a choice structure $(\mathscr{B},C(.))$ we can construct a preference align with this structure, write it as $\succcurlyeq^C$ defined as x\succcurlyeq^C y\Leftrightarrow \exists B \in \mathscr{...
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### Prove that any lexicographic preference $(u_1,u_2)$ must be complete and transitive

Let $\succsim$ be a lexicographic preference represented with $(u_1,u_2)$. $x\succsim y$ if $u_1(x)>u_1(y)$ OR $u_1(x)=u_1(y)$ and $u_2(x)\geq u_2(y)$. Is it obvious that $\succsim$ must be both ...
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1 vote
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### What economic theory models describe a financial regulator's decision to monitor a company?

Let's consider an example (that may not describe how these entities actually work, but humor me): You are the Financial Stability Board (FSB), you need to designate systemically important financial ...
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### Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
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### Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
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### Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries

I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my ...
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### Decision theory: elicitation method

I'm stuck with the following question: Let's say that C1, C2 and C3 represent the certainty equivalents and (x,p,y) the prospects. C1 ~ (x, p, 0) C2 ~ (x, p, C1) C3 ~ (C1, p, 0) What is C3 such that ...
81 views

### Proving the Choice with Recommendations

Suppose that there are two types of outcomes, i.e. $X=X_1 \cup X_2$ with $X_1 \cap X_2=∅$. All outcomes in $X_2$ are the same to the decision maker (he doesn't understand these kind of products). He ...
1 vote
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### Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete?

Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete? By looking at the completeness definition in preference: Definition 1.1(c), this is same as the connected relation in the ...
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### Can a business's search for profits be considered as movement in state space?

When businesses make decisions to increase profits, they have to adjust several "parameters" of the business such as quantity to output, pricing, choosing a production mix, brand positioning,...
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### What does the Arrow-Pratt risk aversion measure mean in the deterministic case?

What type of preferences that are not related to risk aversion can the Arrow-Pratt measure of absolute (or relative) risk aversion model? So far, it seems to me that low RRA/ARA preferences imply that ...
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### Proof of First-Order Stochastic Dominance with Riemann Sums

Let $A = \mathbb{R}$. For $p,q\in \mathcal{L}(A)$, $p$ first-order stochastically dominates (FOSD) $q$ if $F_p(a)-F_q(a) \leq 0, \forall a\in A$. Show that $p$ first-order stochastically dominates $q$ ...
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### Choice theory vs decision theory

I always thought that Decision Theory and Choice Theory are the same fields. But when reading the Wikipedia entry for Decision Theory recently, I read the explicit clarification: "not to be ...
120 views

### What is the economic intuition of prudence in the static case?

How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)? I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
1 vote
69 views

### What is the risk aversion domain and how this could change in a dynamic market game?

Most of the market microstructure theory models assume a risk aversion coefficient, say $\gamma$ that is indexed with $i$ since any individual $i$ has her own $\gamma_i$ coefficient. Also, the inverse ...
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