<p>AA approach appears to follow two stages: first, &quot;nature&quot; provides which event obtains, which results in the given lottery; second, the lottery is resolved, therefore revealing the intrinsic probabilities. AA suggests to resolve by backward induction. Under usual conditions for vNM utility, agent may define a function for her utility.</p>
<p>I found a nice paper comparing Savage vs. AA approaches, from which I got this construction, e.g. see Fig. 1 and 2. I hope it helps.
<a href="https://link.springer.com/article/10.1007/s11166-018-9273-7" rel="nofollow noreferrer">https://link.springer.com/article/10.1007/s11166-018-9273-7</a></p>

CC BY-SA 4.0
2020-09-27T09:05:25.397Z
Hi! In its current form this is a link only answer. These are not encouraged; please copy the gist of the relevant information into the body of your answer. (Perhaps the abstract?)
Giskard
CC BY-SA 4.0
2020-09-27T08:46:32.727Z
2020-09-27T11:26:16.493Z
2020-09-27T11:26:16.493Z
aatr
<p>I would like to hopefully get some insights on the Anscombe and Aumann Expected utility.</p>

<p>I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers preferences over not pre-determined lotteries or risky outcomes.</p>

<p>However, I don't manage to rationalize this way the Anscombe and Aumann expected utility, although I believe I understand the proof.</p>

<p>Particularly, I would like to know how I can rely heuristically the 'state space' and 'probability spaces' (other than being antecedent and image of the Aumann act).</p>

<p>Also, sometimes 'objective probabilities' are evoked as well as an explanation with horses, that I don't get.</p>

<p>Sorry for this confusing message and thanks a lot!</p>

<microeconomics><mathematical-economics><decision-theory><expected-utility><measuring-utility>
Anscombe and Auman Expected Utility
Rororo
# Anscombe and Auman Expected Utility

(Asked by: username_0 on 2018-10-04)

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility.

I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers preferences over not pre-determined lotteries or risky outcomes.

However, I don't manage to rationalize this way the Anscombe and Aumann expected utility, although I believe I understand the proof.

Particularly, I would like to know how I can rely heuristically the 'state space' and 'probability spaces' (other than being antecedent and image of the Aumann act).

Also, sometimes 'objective probabilities' are evoked as well as an explanation with horses, that I don't get.

Sorry for this confusing message and thanks a lot!

**Tags:** microeconomics, mathematical-economics, decision-theory, expected-utility, measuring-utility

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## 1 answers

### Answer by username_1 on 2020-09-27. Score: 1

AA approach appears to follow two stages: first, "nature" provides which event obtains, which results in the given lottery; second, the lottery is resolved, therefore revealing the intrinsic probabilities. AA suggests to resolve by backward induction. Under usual conditions for vNM utility, agent may define a function for her utility.

I found a nice paper comparing Savage vs. AA approaches, from which I got this construction, e.g. see Fig. 1 and 2. I hope it helps.
<https://link.springer.com/article/10.1007/s11166-018-9273-7>

> **Comments:**
> **username_2**: Hi! In its current form this is a link only answer. These are not encouraged; please copy the gist of the relevant information into the body of your answer. (Perhaps the abstract?)  

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