3 votes

Decision theory: elicitation method

If you receive $C3$, you get lottery $C_1$ with probability $p$ and $0$ with probability $(1-p)$. $C_1$ is the lottery that gives $x$ with probability $p$ and $0$ with probability $(1-p)$. So in total,...
tdm's user avatar
  • 12k
2 votes

What is the difference between utility, payoff and expected utility, or are the terms interchangeable?

"Utility" is a foundational concept, a nomenclature label to name what we experience from our interaction with tangible things or intangible phenomena, situations etc. So e.g. "...
Alecos Papadopoulos's user avatar
2 votes
Accepted

About Theorem 1.1 (the Expected-Utility Maximization Theorem) in Game Theory: Analysis of Conflict by Roger Myerson

Let's first have a look at the left hand side of the equation. Take an outcome $y$ and a state $r$. There are two cases: If $y$ is not the worst outcome in state $r$ then the lottery gives: $$ \left(\...
tdm's user avatar
  • 12k
2 votes

How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

That is hopeless. The preference order over certain outcomes determines the preferences over every compatible expected utility representation if and only if there are at most two indifference classes. ...
Michael Greinecker's user avatar
1 vote

Ratio of two Jensen inequality

A bit of a "non answer" but it appears that you cant say anything about how the a ratio of expectations is related to an expectation of ratios. To illustrate, let $f(X)$ and $g(X)$ be ...
EconJohn's user avatar
  • 8,345
1 vote
Accepted

Ratio of two Jensen inequality

If $X$ and $Y$ are independent positive random variables then the following are true by Jensen's Inequality: \begin{eqnarray*} \mathbb{E}\left(\dfrac{X}{Y}\right) \underbrace{=}_{\text{By Independence}...
Amit's user avatar
  • 8,466
1 vote

What is the difference between utility, payoff and expected utility, or are the terms interchangeable?

Players in game theory are assumed to have preferences over the possible outcomes of a game. Players are also assumed to adhere to the axioms of Expected Utitilty Theory, so in the presence of risk, ...
VARulle's user avatar
  • 6,805
1 vote
Accepted

Proof of the Lucas' Cost of Business Cycles

I'll first present the assumptions Lucas made. First assume $$ c_t = Ae^{\mu t}e^{-(1/2)\sigma^2}\varepsilon_t, $$ where $\log \varepsilon_t \sim N(0, \sigma^2)$. Under these assumptions, we have $\...
Wittgenstein's Poker's user avatar

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