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Can someone possibly explain how to >>make sense<< of the following identity:

$\int \frac{\partial \ max_d \{ u(x,d) + \epsilon(d) \} }{\partial u(x,d)} q(d\epsilon \lvert x) = \int I\{d = \arg \max_h [u(x,h) + \epsilon(h)] \} q(d \epsilon \lvert x)$

I completely fail to see how taking the partial derivative under the first integral results in the expression with the indicator function?

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  • $\begingroup$ You can edit your own question to fix that $\endgroup$
    – Hushus46
    May 17, 2015 at 21:13

1 Answer 1

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The expression simply says that when you change a function, u(x,d), you only change the max of that function if you change u(x,d*) where d* is the argmax of u(x,d) with respect to d.

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  • $\begingroup$ Very nice explanation thx Mr. Plum $\endgroup$ May 18, 2015 at 10:31

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