# 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 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 ...
149 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 ...
64 views

### 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 ...
34 views

### 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 ...
80 views

### 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 ...
132 views

### 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. ...
36 views

### 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: ...
54 views

### 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, ...
180 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?
42 views

### 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-...
43 views

### 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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### 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 ...
74 views

### 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 ...
20 views

### Original formulation of the axioms of rationality [duplicate]

Completeness and transitivity are considered to be the two axioms of rationality in case of decisions under certainty. I wanted to know when were these axioms first proposed, by whom and the first ...
40 views

### Ranked choice preference with ties - Arrow's Impossibility Theorem

My question relates to my understanding of Arrow's Impossibility Theorem and ranked choice. It seems to me that the requirements on social choice functions are too strict. A social choice function ...
37 views

### Identifiability of Non-Parametric Utility Function?

I recently learned that EU characterized by independence and weak ordering is identifiable, but a utility function like: $U(x)=v_1(x)v_2(x)$ is not identifiable. Does it mean that "cardinal ...
54 views

### If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?

Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that there is a rational preference relation $\succsim$ over simple lotteries. I know that if ...
112 views

Let $U:\mathbb R^2\to\mathbb R$ be a utility function. If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,... 0answers 72 views ### Who were the first economists arguing that utility maximization is the core of rationality and economic behavior? I am looking for the first economists arguing that maximizing utility function is the iff condition of rational behavior. I've learned that neoclassical economics is founded on this argument. Is this ... 3answers 216 views ### 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 ... 1answer 473 views ### Why utility should be bounded (or unbounded)? For Expected Utility and SEU, people make axioms to ensure that the utility is bounded. However, I personally believe that the utility function must be unbounded, especially if we are considering ... 0answers 86 views ### What is the observable definition of "preference" by Frisch? To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations! How to define ... 1answer 89 views ### What additional axiom to GARP do we need to generate a differentiable or smooth utility function After researching for a while, I find this: https://www.jstor.org/stable/1913607?seq=2#metadata_info_tab_contents They come up with an axiom called SSARP that generates a preference with smooth demand ... 1answer 57 views ### Blackwell order of information structures Consider a model where a decision maker (DM) has to choose action y\in \mathcal{Y} possibly without being fully aware of the state of the world. The state of the world has support \mathcal{V}. ... 2answers 79 views ### Can mixed strategies actually predict behaviour of rational actors in non-constant sum games? I understand how the concept of the mixed NE (mathematically) works. But I don’t understand how we can expect players to behave in a way that would arrive at such an equilibrium. Consider the ... 1answer 136 views ### How is the defintion of the mean preserving spread (MPS) not too general? The mean preserving spread is defined as follows: Consider two lotteries g and h. Let x_g und x_h denote the corresponding random variables. Then h is a mean preserving spread (MPS) of g, if: ... 2answers 825 views ### What is the definition of: 'commodity space'? I have seen the concept of commodity space being used multiple times in economics, in particular within microeconomics, but I could not find a general definition of it. Based on the examples that I ... 0answers 42 views ### a\geq 0, x\succsim y implies x+a\succsim y+a so the preference is linear? \succsim is a continuous and local non-satiate weak order. x,y,a are vectors in \mathbb R^n We say a\geq0 if all directions of the vector a is greater or equal to zero. We want to prove (... 1answer 124 views ### Continuity of preferences Let \succsim be a transitive and reflexive relation on a metric space X with closed upper and lower contour sets. If \succsim is not complete, does it hold that: for all converging sequences ... 1answer 48 views ### Example of information structure in a one-player Bayes Correlated Equilibrium Model 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. The state of the world has support \mathcal{... 1answer 47 views ### Write search model as a signal density inducing posterior belief 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 ... 1answer 113 views ### Set of Bayes Correlated Equilibria when complete information is not available Model 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. The state of the world has support \mathcal{... 1answer 51 views ### Minimizing consumption in a single market( Partial Equilibrium) Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market. We know that prohibiting it( ... 2answers 81 views ### 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}. ... 1answer 51 views ### The assumptions of Rational Expectations Models What are the assumptions between rational expectations models and how restricted are there for the following results of economic theory? Where can I find them all gathered in some textbook or in the ... 1answer 56 views ### Risk neutrality in single-agent choice problem under uncertainity Consider the following static single-agent choice problem under uncertainty. Let V be the state of the world with support \mathcal{V} and probability distribution P_V\in \Delta(\mathcal{V}). ... 1answer 109 views ### Consider the utility function U(x,y) = y√x [closed] Draw the indifference curve for U= 10, U=15, U=20. My knowledge of algebra has deteriorated over the last few years of being out of school and I am really unsure of how to answer this. The X value ... 2answers 159 views ### 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 ... 1answer 41 views ### Rigorously Defining Newcomb's "Paradox" I was surprised to find that we did not have a question on this Stack Exchange on this particular problem in decision theory. So I have chosen to add a question on Newcomb's Paradox, though I would ... 1answer 63 views ### Is the set of optimal strategies convex in a single-agent decision choice problem? EDITED with insights from the comment below. Consider a decision maker who has to choose an action among \mathcal{Y}\equiv \{1,2,...,L\}. The payoff from choosing action y\in \mathcal{Y} depends ... 1answer 19 views ### Existence of optimal strategy in a choice problem with uncertainty and information structure Consider a decision maker choosing an action, y, from the finiteset \mathcal{Y}, possibly without having complete information about the state of the world. More precisely, let V be a ... 1answer 152 views ### Boots' Theory by Pratchett Consider the following quote from the book, \textit{Men at Arms} by Terry Pratchett. “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money. ... 1answer 47 views ### Robust predictions in single-agent decision problem with uncertainty I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ... 1answer 49 views ### Optimal strategy in a single-agent choice problem under uncertainty Consider the following single-agent choice problem under uncertainty. Let V be the state of the world with support \mathcal{V} and probability distribution P_V\in \Delta(\mathcal{v}). First, ... 2answers 81 views ### In what kind of economic environment would the cliche of "keeping money under the mattress" be warranted? I'm trying to apply (ideally empirical-backed) economic theory to an age-old cliche. We must be very articulate about the assumptions, because if it's a total collapse of the dollar, then that ... 1answer 125 views ### A weaker definition of local non-satiation can also imply indifference "curve" Let u be a continuous utility function on \mathbb R^2_+\setminus\{0\}. Consider the following three conditions: Local non satiation says that for any x \in X and \epsilon > 0, there exists ... 0answers 47 views ### Rotation of Quasilinear Utility Let u(x,y)=f(x)+y be a quasilinear utility. Now we rotate it by 45 degrees, (such that the x-axis becomes the direction of (1,1)) v(x,y)=f(x-y)+x+y. Is v also a quasilinear utility? What is ... 1answer 169 views ### Demand correspondence is both upper and lower hemi-continuous; is the preference continuous? \succsim is a weak order over \mathbb R^L. For a closed budget set B\subset\mathbb R^L, define demand correspondence:$$D(B)=\{x\in B|x\succsim y\forall y\in B\}. We know that $D$ is always ...
GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
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 ...