Using array_intersect on a multi-dimensional array

I have two arrays that both look like this:

Array
(
    [0] => Array
        (
            [name] => STRING
            [value] => STRING
        )

    [1] => Array
        (
            [name] => STRING
            [value] => STRING
        )

    [2] => Array
        (
            [name] => STRING
            [value] => STRING
        )
)

and I would like to be able to replicate array_intersect by comparing the ID of the sub arrays within the two master arrays. So far, I haven't been successful in my attempts. :(