One is to pick a very frothy market. For instance, about 10 years ago I acquired a preorder for four Butterfly Labs Bitcoin miners shortly before they were to ship (months behind schedule but with the queue starting to ship). About a month later, received them. Sold them. Made a nice tidy profit. This was definitely speculation, but market timing worked in my favor. It could as easily have not.
Second is one of my side projects I call "grains of rice". Everyone's pretty familiar with the cost of a sack of rice, but consider if your customer wanted just one grain. One grain total. Not interested in extras, no room for 'em. Just want the one. That grain of rice suddenly gets pretty expensive, as in hundreds, thousands, even tens of thousands, of dollars per pound shipped.
There's additional packaging involved, and the frictional cost of shipping, and additional handling and listing costs involved, but it's pretty easy to buy things for $5 a dozen and sell them for $0.99 a pop. You can get an additional leg up by warehousing and shipping closer and faster than your source, meaning your customers paying your premium only wait the 3 days instead of the 3 weeks it took you to get it.
That's not pure arbitrage, as you are adding value by wholesaling, splitting things up, and repackaging, but it's not uncommon to have eBay on one or both ends of a successful corresponding transaction.
A year later I did a similar thing with "anti-snoring mouthpieces". The product was effectively a mouthguard, a popsicle sticks, and instructions for molding it. A few branded companies were selling this product for $80. I imported the exact same product from Alibaba for $3 each and sold them on eBay for $15 each. I had a box of 300 of them and every day I would put one or two envelopes in the mail until the box was empty.
If so, that leads to such sub-questions as:
How did you know/learn that you could make a profit on that item?
What kind of profit did you make?
How long did you have to wait to sell the item, that is, what was the turn-around time, etc.
(Inquiring minds want to know! :-))
After I've secured one for myself to keep, there's a short-ish period of time during which I feel like an expert on the market for that item, and my "Saved Search" with email notification remains enabled. Sometimes obviously underpriced listings(s) then show up. Not much more to it than that.
Hardly anybody uses auction format anymore for anything but rarities/collectibles.
Sounds sad.
So given those parameters, which coin would someone pick, and why? See, that's a form of arbitrage, because you're buying something on eBay and selling it back on eBay.
The idea that "some poor third party sap" is paying more is not correct, because the second buyer of the coin is presumably paying MARKET VALUE for the coin, and presumably can sell it again at market value (no loss), and can possibly even wait some time for the coin to appreciate again.
In a free market people exchange goods for however much money they value the goods at. The prices (price = what people value something at) of some of those items are in constant flux, thus there become opportunities for arbitrage. People in the financial community already know this, although they don't apply those principles to eBay.
No single person is a sap, people just a) Value (assign price to) things differently and b) Have different abilities to pay, i.e., Bill Gates could pay a whole lot more for something than say, someone living in a third-world country...