How does the Arena work?

The answer is almost certainly "No". It's been proven that the list of opponents is all taken from a stored list of names within the game client. Check the next time you play; for me on Android the last letter of the name is cut off, but every single "player" I see is on that list. An EA representative tried to claim they replace the name of the actual "Player" with one of these to ensure no abusive names slip through. However if you follow one of the online recommended builds for Arena so you have the best chance of winning, you'll find it's also set to scale so each match is harder than the last, with you normally losing around the second game of the second run. Every week, every time. So at the most charitable interpretation possible, they're sampling a final score from the player base, changing their name to the pre-selected list, then ensuring one at a fixed point is impossible to beat.

More likely, it's not a multiplayer service at all.

Which makes how when the week is getting close to an end, one of the players in the last few hours is suddenly pushing to beat your league ranking. Better spend some gems to keep your place and reward, eh? What's that, out of gems. Why the real money store is just over here...

When I realised this is what they were doing, I stopped playing.