# Tag Info

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The expected utility theorem (EUT), first and foremost, establishes a utility representation of the preference over lotteries. This is akin to establishing utility representation of preference over deterministic consumption bundles in consumer theory. The representation (in both cases) is valuable because it gives us tools like algebra and calculus to do ...

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Let $n \geq 2$. Observe that $$\mathbb{E}[u_i] = \mathbb{E}[u_i|v_i > r]P(v_i > r) + \mathbb{E}[u_i|v_i \leq r]P(v_i \leq r) = \mathbb{E}[u_i|v_i > r]P(v_i > r)$$ since $\mathbb{E}[u_i|v_i \leq r] = 0$. Moreover, $P(v_i > r) = 1 - r$ if the values are standard uniform. So to compute the expected payoff $\mathbb{E}[u_i]$, all that remains is ...

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We don't use the EUT for comparing lotteries with close probabilities, except if we are solving an exercise involving an Allais paradox type of question. We don't actually use it at all if we are not theorists trying to prove something. The EUT tells you that if you have preferences over lotteries satisfying the basic axioms, including independence, then ...

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