Questions tagged [expected-utility]
The expected utility theory deals with the analysis of choices among risky projects with multiple possible outcomes.
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Convexity of indirect utility in probabilities
I am interested in the concavity in $p$ of the indirect utility function
$$V(p,W)=max_{x,y,z} pf_1(x,y)+(1-p)f_2(x,z)$$
under the constraint
$$x+py+(1-p)z=W$$
where $0<p<1$ and where $f_1,f_2$ ...
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vNM theorem for finitely additive measure?
The main difference between vNM EU and Savage SEU is that one is objective one is subjective.
However, there is another difference: vNM EU uses countably additive prob while Savage use finitely ...
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what are stakes in cost-benefit terms? Clarifying five examples/contentions
Please excuse me if this is off-topic, and don't be offended if it is stupid.
Scholars theorize that the stakes matter for rational decision making or cost-benefit calculations (under uncertainty or ...
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Lucas 1972 Neutrality of Money Proof of derivation
Lucas (1972) Neutrality of Money section 3 has following set up.
$U(c,n)$ is Utility function of consumption and labor (or producing labor output). $U_c (c,n) >0$ and $U_n (c,n)<0$. Further, the ...
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how to reach Continuous Expected Utility (EU)?
Consider EU on monetary outcomes. Say we have a utility function $u:\mathbb R\to\mathbb R$
The common axioms of EU are continuity, independence and weak order.
These axioms do not imply that the ...
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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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A Measure Theory\Probability Question Regarding Model Setting of Ambiguity (Schmeidler (1984, 1989))
In David Schmeidler (1984), "Subjective Probability and Expected Utility without Additivity", "2. Axioms and Background", there is a setting:
Let $X$ be a set and let $Y$ be the ...
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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 ...
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Can we use the utility of discounted flows to do asset pricing?
Is it possible to do asset pricing by using the expected utility of the present value of all future discounted cash flows ? I aim to use this utility function to define an optimal portfolio, but I ...
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Degrees of Risk aversion and Expected utility [closed]
There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
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Comparing agent decision-making under risk-neutrality and risk-Aversion
I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows:
There is a technology (for example, a vaccine) which reduces the ...
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How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?
Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
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How special is the "expected value" operator in Von Neumann–Morgenstern utility theorem?
The Von Neumann–Morgenstern utility theorem states that
For any VNM-rational agent (i.e. satisfying axioms 1–4), there exists a function $u$ which assigns to each outcome $A$ a real number $u(A)$ ...
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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 ...
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Bernoulli, Ergodicity, Ole Peters
You may or may not be aware that there's a Simple English Wikipedia.
It's very helpful for those of us who know English, but are unable to parse complex sentences (for whatever reason).
I'm very ...
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What is the relation between Blackwell's order and Stochastic Dominance order?
In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
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Ratio of two Jensen inequality
I have these pair of numbers
$ (a, b) = (\frac{4}{9}, \frac{1}{9}) $ and $(c, d) = (\frac{1}{2}, \frac{1}{6}) $. (Number mean nothing, just for illustration and simplification)
Note that - (a, b) are ...
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What does the empirical literature tell us about the relative merits of alternative functional forms describing the marginal utility of income?
Among the various functional forms that have been used on model the marginal utility of income in, e.g., in making decisions under uncertainty, and perhaps intertemporal choice as well, is the ...
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About Theorem 1.1 (the Expected-Utility Maximization Theorem) in Game Theory: Analysis of Conflict by Roger Myerson
I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his proof of Theorem 1.1, the Expected-Utility Maximization Theorem. The Theorem goes ...
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What is the difference between utility, payoff and expected utility, or are the terms interchangeable?
I've started teaching myself game theory recently, but so far I haven't come across anything clarifying these terms .
This is my understanding of the terms based on what I know:
Payoff = Utility. ...
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Proof of the Lucas' Cost of Business Cycles
I am trying to derive the parameter used by Lucas to measure the cost of business cycles, namely:
derived in the paper "Macroeconomic Priorities".
I already searched in several papers but I ...
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Expected utility maximization question
If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ...
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Deriving the CAPM: going from utility of consumption to utility of asset returns
Some textbook presentations of the capital asset pricing model (CAPM) take returns on stocks as a primitive and proceed as if agents derive utility from asset returns. Assuming a concave utility ...
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Expected Utility
I really don't know how to interpret the graph. Can someone help me?
I thought of doing 0.6253+0.3751 to find the expected value of the lottery but where is the sure bet?
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Existence of best and worst lotteries with finite outcome set and IIA
In the context of expected utility theory, I want to prove that if the set of outcomes is finite and an agent has a rational preference relation over the set of lotteries, and if that preference ...
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Expected revenue maximizing auction & ex-post efficiency
Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?
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Convergence of various forms of Prospect Theory?
I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience.
My problem is the following: I want to analyse the effects ...
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Von Neumann-Morgenstern Utility Theory Question
There's a question in my ECON notes that I don't understand, any help would be greatly appreciated.
Here are the definitions used about VNM Utility Theory.
The question is posted after the definitions....
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Expected value inside a utility function
Lets say Agent 1 has a utility function that depends on the other person, i.e., $u_1(x_1-x_2)$, where $x_i$ is the choice of Agent $i$. Suppose the expected value of $x_2$ is denoted $E[x_2]$.
Can $...
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On risk aversion and validity of utility functions
Question
A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences.
The investor has a current ...
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Mixed strategy in extensive form games with complete and perfect information
I saw the lemma:
"In extensive form games with complete and perfect information, any mixed strategy
for player i will result in a lower or equal utility for player i compared to some pure ...
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Experimenting with Mean Variance Analysis
here with a question about mean-variance analysis and utility theory hope you can help me.
First point
My main objetive is to maximize the expected utility from portfolios given by $\sigma_p^2=\frac{C}...
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Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?
Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU?
To my knowledge, most utility functions under risk and ...
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Utility of both players in St. Petersbourg paradox - behavioural economics
Im reading a paper by Karl Menger [1] about the St. Peterbourg paradox :
In the theory of probability, the "Petersburg Game" designates the
follow- ing gamei between two persons, A and B. ...
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What is the intuition behind Expected Utility Theorem?
I am referring to the definition in Proposition 6.B.3 on Page 176 of Mas Colell. I follow the formal proof and the application of the Independence axiom at various steps (mathematical application of ...
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certainty equivalent and lotteries [closed]
suppose an agent has $u(z)=-e^{-bz}$ where $b>0$ as her Bernoulli utility function and faces two gambles:
G1: win 1000 dollars with probability $\frac{1}{2}$ and zero with probability $\frac{1}{2}$ ...
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What is the expected payoff for a bidder in a second-price auction with N uniform distributed bidders, when the auctioneer sets a reserve price?
I would like to know what bidder i's expected payoff looks like in a second-price auction with $N=\{1,2,...,n\}$ bidders, where each bidder $i\in N$ has independent and uniform distributed valuations $...
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Model the uncertain impact of a proposed policy by expected utility or other probabilistic approach
The impact of a proposed policy is often uncertain and subjected to randomness. As such, it seems natural to use probabilistic models. How to model the policy impact using the expected utility ...
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How does this imply that a Pareto optimum maximizes a weighted average of utility functions?
I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me.
In the passage, Back is ...
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Von Neuman-Morgenstern utility theorem apply only to linear utility functions?
Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...
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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 would be the Dual Expected Utility function for an English Auction?
So the DEU function is $$V(p)= \Sigma \,x_i\pi_i(p),$$ and since an auction only has two outcomes for a bidder, failure (with probability $p$) or success (probability $1-p$) the function becomes $$V(p)...
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What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?
Peters (2019) made a splash criticizing the theory of expected utility on the grounds that it implicitly assumes ergodicity where this is unwarranted. He stated this applies widely in economics, to ...
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Deducing beliefs from choices when the Savage Axioms are true
We know, that given a set of possible outcomes $X$, a set of states of nature $\Omega$, and the set of all acts from $\Omega$ to $X$, if a DM has rational preferences over the acts and if the Savage ...
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Repeated betting game with positive expected value
Consider the following basic repeated betting game:
A player can enter the game with an amount of money x.
The game consists of multiple rounds.
In each round a ...
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Expected utility theory (Lottery notation)
A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences
$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$
...
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Comparing & contrasting decision problems and normal games
I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.
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Why utility rather than expected utility in Cochrane's "Asset Pricing"?
Cochrane "Asset Pricing" Chapter 1 p. 6 says
We model investors by a utility function defined over current and future values of consumption,
$$
U(c_t,c_{t+1}) = u(c_t) + \beta \mathbb{E_t}[...
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Is the expected utility the inverse of the utility function?
Can somebody explain to me if that it's true and also graphically explain it?
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