There's a great short story about a similar premise by Ted Chiang (the guy who wrote the story that Arrival is based on).
If you don't own the book it appears in -- LaVar Burton reads it in full on his podcast.
The merchant and the alchemist's gate
https://www.stitcher.com/show/levar...lchemists-gate-part-1-by-ted-chiang-200144201
LeVar Burton Reads
Listen to LeVar Burton Reads on Pandora - The best short fiction, handpicked by the best voice in podcasting and presented in 3D immersive audio. In every episode, host LeVar Burton (Roots, Reading Rainbow, Star Trek) invites you to take a break from your daily life, and dive into a great story...www.stitcher.com
(2 parts. It has to do with the complication that your future self would have also seen the tape)
This is one of my favorite novellas! It's a beautiful story.