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And who gets the profits from the bots?

Whoever runs them, but it's usually pretty small. The prices are roughly in line, people are picking up pennies. If the profits are large, then I would encourage you to do the same thing and get your share (doesn't even necessarily have to be a bot, you can just trade manually if there is a large abitrage and you think you can make money from it). This will help keep the prices even more in line.

And to be explicit, I don't run any of these arbitrage bots, I don't know who runs any of them. I don't benefit in any way if they make money.

I do run a market maker bot that does nothing but trade neutral (buying and selling equal amounts) to keep the spread in the internal market low. It also has all activity on chain so it is transparent (@teamsmooth-mm).

Thanks, explicit answer!