Another spin on the recent question How would you bring wealth back to the past?, this one will attempt to look at the effect on collectibles.
Almost by definitions, things are collectible because there are not many of them. There were hundreds of thousands of copies of Action Comics #1 at the time of printing, now there are a few dozen. The same is true of most rare collectibles. For whatever reasons, people didn't keep them, they were thrown away, they broke, etc. And now people are willing to pay through the nose for one.
But with time travel, I could take twenty dollars in period cash, buy two hundred copies of Action #1, come back as a millionaire.
But would I? first off, two hundred copies would depress the price, as the rarity has now greatly decreased. OK, no problem, go private sale, to people who wouldn't let anyone know they had a copy.
But at what point could the number of people going back and snapping all the Butcher cover Beatles albums actually cause a shortage IN the past? It'll get quite complex trying to make sure you don't accidentally buy the physical copy of some rare book that ends up in the Smithsonian, for example.
What are some of the checks and balances you could envision to keep the collectors' market from collapsing?