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Aug 22, 2019 at 12:05 comment added Star Could you help me with this question here economics.stackexchange.com/questions/30601/…? I think it is related to what you were pointing out in your answer here, but I want to understand it more formally.
Jun 26, 2019 at 17:20 vote accept Star
Jun 26, 2019 at 17:14 comment added Regio the only thing I mean my "circumvents..." is that you don't have to specify, that the solution is a measure $P_Y$ such that for all $y$ with $P_Y(y)>0$ and for all $\tilde y\neq y$ ...". I.e. the only thing I mean to say is that the maximization is more clear.
Jun 26, 2019 at 17:12 comment added Regio No, it is not enough. I think I now understand your utility. What you are assuming is that there are three random variables and I need to choose one of them. its realization wil be my payoff. The optimal decision will be to choose the random variable with the highest expected payoff given the prior. Suppose that the prior is such that the expected values of each of them are $E(v_1)=5, E(v_2)=3, E(v_3)=5$ then the solution is not unique. It is pretty easy to think of examples where two or more random variables have the same mean (it should be clear that normality does not help here).
Jun 26, 2019 at 12:04 comment added Star What do you mean by "and circumvents the need to specify the quantifiers"?
Jun 26, 2019 at 10:22 comment added Star Thanks. Regarding the last point, in my example I have $u(y,v)\equiv v_y$ where $v\equiv (v_1,v_2,v_3)$. Is that enough for uniqueness?
Jun 25, 2019 at 23:00 history answered Regio CC BY-SA 4.0