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I don't have 2 data sets. I don't have a target and a universe. I only have a single set from which I've created centroids, and trade areas off those centroids. Want to know where the trade areas intersect.
In your case, feed the records into both the Target and Universe Inputs of the Spatial Match tool. It will spit out pairs of trade areas that intersect. After removing the records when the a trade area intersects itself, use a Spatial Process to create the intersections.