# 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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### Risk Aversion under Worst Case Utility Representation

The preference relations (≿A and ≿B) over lotteries is defined as: p ≿ q iff min{v(z) : p(z) > 0} ≥ min{v(z) : q(z) > 0} Under what conditions can you say that ≿A is more risk averse than ≿B?
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### Can the Machina Paradox be solved by expanding the choice set?

In another question, the Machina paradox is mentioned as a possible counterexample to the expected utility model: Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-...
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### 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 ...
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### How to determine if people behave optimally with a generic utility function?

I have a some real-world data and a real-world choice for which I know the optimum solution is something like $y^* = u(x)$, where $u(.)$ is some utility function. I have data on $y$ and $x$, so if I ...
157 views

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

When questioning the rational choice hypothesis, I often get responses that are similar to the followings: "Individuals may sometimes make irrational decisions, but a large group of economic ...
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### Can any three of the four vNM axioms (of expected utility theory) be satisfied without satisfying the fourth?

Is it true that any three of the four vNM axioms (of expected utility theory) can be satisfied without satisfying the fourth? Any examples which support such claim? Basically I'd like to prove that ...
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### Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
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### Analyzing a Gambling Race Paradox

Suppose a number of players are given $100$ points each, and repeatedly engage in a gamble having positive expected value, with the goals of being the first player to reach $100000$ points. Solving ...
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### What is the difference between Impression Management and Signaling Theory?

I'm interested in theories on how organisations shape their stakeholders' (especially consumers' and investors') perceptions and decisions. I read about Impression Management and Signaling Theory. ...
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### 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 $\mathcal{V}$. ...
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### Axiom of Minimal Liberalism & Sen's Theorem of Paretial Liberal

Suppose that a person believes that all humans are guaranteed a set of rights that cannot be taken from them in any situation or circumstance (for example, the right to marry a person of your choice, ...
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### Pure Nash equilibrium in bidding game?

According to the answer key for a problem set, there is no pure strategy Nash equilibrium in the following problem. Yet I can't see why not. Could it be an error in the answer key? Here's the problem: ...
188 views

### Question about Social Welfare Function and Social Profile

What are the meanings of a social welfare function and social profile? How are they related?
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### If I had a new economical theory, how could I share it with academical environments? I call it “algorythmic economy”

If I had a new economical theory, how could I share it with academical environments? I call it algorythmic economy. I have made this same question on Quora. https://www.quora.com/unanswered/If-I-had-a-...
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### Definition of strictly convex preference

Let $x,y\in X$. Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that: $x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?
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### GARP and SARP assumed mononticity?

Monotonicity means the decision maker prefer more goods than less. It is not mentioned in textbook that SARP and GARP preasumed monotonicity, implicitly. GARP: if $a$ is indirectly revealed preferred ...
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### Ordinally Separable Utility Representation

Let $X_i$ be a separable, compact, Banach space. Definition: A weak order $\succeq$ on $X=\prod_{i=1}^NX_i$ has an ordinally separable representation if there exists $u_i: X\rightarrow \mathbb{R}$ and ...
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### 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 effectively incentivize the subjects to not to adopt mixed strategy? I would like to re-emphasize that the question in concern is "how to prevent people ...
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### Can I rename a utility function based on its properties?

A big name researcher gives a name to a specific utility function 30 years ago. Now I am writing a paper and feel that a new name might be more suited because of the properties associated with the ...
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### What are good mathematics books to learn decision theory?

I am looking for a set of mathematics books to understand proofs in decision theory. Examples would be proofs of utility representations and social choice (im-)possibility results. I found many ...
Consider a decision maker (DM) who as to choose an action from the finite set $\mathcal{Y}$ with cardinality $L.$ The payoff the he gets depends on the action chosen and the state of the world. The ...