Questions tagged [expected-utility]

The expected utility theory deals with the analysis of choices among risky projects with multiple possible outcomes.

Filter by
Sorted by
Tagged with
2 votes
0 answers
54 views

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 ...
user avatar
2 votes
1 answer
75 views

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 ...
user avatar
2 votes
0 answers
51 views

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}...
user avatar
0 votes
0 answers
28 views

Is it possible to have mean-variance preferences with different states of nature? Mean-Variance and Expected utility together?

I have to maximize mean-variance preferences like this (where Pi is a profit function): \begin{align} \label{eq:9} \max\limits_{Q_{F}^{\{x\}}}Z_{w}= E[\pi{\{x\}}]-\frac{A}{2}Var[\pi{\{x\}}] \nonumber\\...
user avatar
4 votes
1 answer
97 views

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 ...
user avatar
  • 1,656
1 vote
0 answers
58 views

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. ...
user avatar
4 votes
2 answers
187 views

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 ...
user avatar
  • 923
1 vote
1 answer
53 views

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 $\frac{1}{2}$ ...
user avatar
1 vote
1 answer
99 views

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 $...
user avatar
3 votes
0 answers
42 views

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 ...
user avatar
0 votes
0 answers
19 views

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 ...
user avatar
  • 111
0 votes
0 answers
17 views

Could Allais Paradox and similar experiments be harmonized with expected utility theory by noting additional counterparty risks?

My answers to the initial formulations of Allais Paradox are 1B and 2B, but only for setups where I have a high degree of confidence in the method of randomness being employed. In many if not most ...
user avatar
2 votes
1 answer
115 views

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 ...
user avatar
0 votes
0 answers
40 views

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 ...
user avatar
  • 448
2 votes
1 answer
82 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 ...
user avatar
3 votes
1 answer
46 views

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)...
user avatar
10 votes
3 answers
1k views

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 ...
user avatar
2 votes
0 answers
37 views

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 ...
user avatar
1 vote
0 answers
35 views

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 ...
user avatar
3 votes
1 answer
168 views

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 $$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ ...
user avatar
1 vote
1 answer
232 views

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.
user avatar
  • 23
4 votes
1 answer
111 views

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}[...
user avatar
-2 votes
1 answer
144 views

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?
user avatar
  • 11
0 votes
1 answer
115 views

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 ...
user avatar
  • 33
1 vote
0 answers
37 views

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: ...
user avatar
1 vote
0 answers
24 views

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 ...
user avatar
  • 11
3 votes
1 answer
303 views

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 ...
user avatar
  • 33
0 votes
2 answers
83 views

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 ...
user avatar
  • 3
0 votes
1 answer
199 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: $...
user avatar
  • 321
0 votes
1 answer
139 views

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 ...
user avatar
1 vote
1 answer
50 views

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 $W$...
user avatar
3 votes
1 answer
134 views

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 ...
user avatar
  • 33
0 votes
1 answer
32 views

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 ...
user avatar
  • 244
4 votes
1 answer
101 views

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 ...
user avatar
  • 1,656
3 votes
1 answer
461 views

Why is the risk premium always positive for risk averse individuals?

I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.
user avatar
3 votes
1 answer
105 views

Intertemporal choice with possibility of death

Here is the setup: Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by: $$...
user avatar
1 vote
1 answer
118 views

Why can we write any lottery as a convex combination of the degenerate lotteries?

I know that a degenerate lottery is a lottery that yields outcome $n$ with probability $1$ and I also know the definition of convex combination: given $x_{1},x_{2}, \cdots ,x_{n} \in \mathbb{R}$, a ...
user avatar
-1 votes
1 answer
207 views

How to prove the relationship between the expected value of a lottery and its certainty equivalent?

Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent). (Definition of $CE$: the ...
user avatar
  • 372
0 votes
1 answer
145 views

Expected Utility and Jensen's Inequality

Consider two random variables (costs and valuations) distributed $v\backsim G(.)$ and $c \backsim F(.)$ with pdfs $g(.)$ and $f(.)$. Let the supports of $c$ and $v$ be $[x,y]$. Let $x<a=E(v)<b&...
user avatar
0 votes
1 answer
119 views

Relationship between expected utility and independence axiom

Jonathan Levin in "Choice under Uncertainty" wrote in Theorem 1 " A complete and transitive preference relation on a set of lotteries P satisfies continuity and independence if and only if it admits ...
user avatar
0 votes
1 answer
1k views

Check if a utility function represents a monotone preference

Given a function $u(x_1, x_2) = x_1 +x_2 + \min(2x_1, x_2)$, how do we mathematically prove that it monotonic or not? Is there is a general algebraic technique to show monotonicity of suchlike ...
user avatar
0 votes
2 answers
154 views

Algebraic approach towards convexity

I have a function: $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
user avatar
2 votes
1 answer
4k views

Local non-satiation in economics

I am having trouble completely understanding the mathematical definition of non-satiation. I have stated the definition from Wikipedia below. It would be great if someone can graphically explain. ...
user avatar
1 vote
0 answers
115 views

derive value function from utility function

We have the utility function. $$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$ And I am trying to find the value function. $U$ is utility function. $c_t$ is consumption at ...
user avatar
5 votes
1 answer
729 views

How does expected utility theory treat losses?

I've been reading about prospect theory lately and have read often that prospect theory predicts people will be risk averse in gains and risk seeking in losses. This statement is typically ...
user avatar
0 votes
0 answers
29 views

Savage's subjective probabilities applied to Allais paradox

I've been reading up on the von-Neumann and Savage proofs for the existence of an expected utility representation. I've also been reading critiques of the expected utility hypothesis, especially the ...
user avatar
  • 129
0 votes
1 answer
240 views

Proof: Risk averse; Certainty Equivalent smaller than expected value

I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds: The certainty equivalent, $CE(\cdot)$, is ...
user avatar
0 votes
1 answer
64 views

Expected Income Question

An urn contains equal number of green and red balls. Suppose you are playing the following game. You draw one ball at random from the urn and note its colour. The ball is then placed back in the urn, ...
user avatar
1 vote
1 answer
105 views

Independence and Reduction Axioms

I have read that the Independence of Irrelevant Alternatives axiom in expected utility theory implies the fact that compound lotteries are equally preferred to their reduced form simple lotteries. ...
user avatar
  • 352
0 votes
1 answer
62 views

First Order Stochastic Domination and lottery preferences

Let $L$,$L'$ be two lotteries over the real numbers. Let $u$ be an increasing Bernoulli utility function. Let $F_L$, $F_{L'}$ be the CDFs of the two lotteries. We wish to show that $$L \succ_{FOSD} L'...
user avatar
  • 352