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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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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 ...
Richard Hardy's user avatar
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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 $\frac{1}{2}$ ...
Mrnobody's user avatar
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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 to empirically measure the underlying utility function for a 'max EU" SWF? Stated/revealed preferences over uncertain lotteries, or?

Direct answers, as well as pointers to the best literature and textbook treatments, as well as the names of key researchers, are appreciated. Suppose we are considering policies and transfers that ...
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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 ...
Nav89's user avatar
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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 ...
Richard Hardy's user avatar
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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 ...
Ishan Kashyap Hazarika's user avatar
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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 $$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ ...
mathstudent23's user avatar
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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}[...
Richard Hardy's user avatar
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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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The efficient frontier in mean variance criterion

The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance,Why do the optimal portfolios in the effcient frontier, is ...
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Need help with Wakker (2010) on arbitrage

In Prospect Theory (2010; Cambridge UP), Peter P. Wakker has an exercise assignment 3.3.6 without solution in the book and I'm really unsure about this one. The exercise states on pages 76-77: ...
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Calculating risk interest rate within a two period model

I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility ...
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Should the "value function" be "utility function" in prospect theory?

I have a background in mathematics rather than economics, and currently reading Choices, Values, and Frames[1]. The paper defines a "hypothetical value function" (the s-shape that is concave ...
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Fair value that a risk averse individual would pay to enter a gamble

Introduction Assuming an individual (or corporation) with risk aversion and a von Neumann-Morgenstern utility curve and given a gamble g with E(g) > 0. From what I researched, certainty equivalent is ...
rmorel's user avatar
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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: $...
Andre's user avatar
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Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?

This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference ...
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1 answer
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Understanding Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion

I am trying to understand Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion. I am struggling to completely understand the following: Suppose you have initial wealth of $W$...
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1 answer
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Diminishing mariginal utility and risk preferences

Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it ...
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If the marginal cost is equal to 1, how does that imply marginal cost is equal to marginal benefit?

The function below is a utility function simplified after subject to an implied participation constraint. $$ E\left(\pi_{n}\right)=e^{*}-E\left(s^{*}\right)=e^{*}-c\left(e^{*}\right) $$ where $ \pi_n ...
aisync's user avatar
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Who is the first one to equate "rational" with "complete and transitive preference"?

MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first? vNM said ...
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