# 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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### 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 ...
1answer
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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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### How to Represent as a Payoff Matrix

I'm trying to represent the following as a pay-off matrix. I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
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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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### Negotiations under expected utility maximization

A buyer is negotiating with a used car salesperson. The value of the car to the seller is uniformly distributed between 0 and 5000. Value to the buyer is 50 percent more than that of the seller (i.e. ...
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### 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 ...
1answer
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### 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 ...
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### Lotteries and expected utility

Suppose we have the following four lotteries: $L_{1}=[(1,\$1)]L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$ $L_{3}=[(0.9,\$0),(0.1,\$5)]$ $L_{4}=[(0.89,\$0),(0.11,\$1)]$ If our agent says that he ...
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### Expected values vs uncertainty

Most models I have seen use expected values. Why is this a better economic model than uncertainty and economic agents thus having to make 'best guesses', with the result of 'animal spirits' playing a ...
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### Literature on Recursive Preferences and Time-Additive Expected Utility

In Chapter 20 of the book Economic Dynamics in Discrete Time, named "Recursive Utility", the author asserts that the Time-Additive Expected Utility Model (TAEU) has some shortcomings when applied to ...
2answers
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### Is there a dutch book argument for the “independence of irrelevant alternatives” axiom?

There is a dutch book argument to show that nontransitive preferences are in a sense "unreasonable", which justifies why we pose the axiom of transitivity in the definition of "rational preferences", ...