"would have to sell for 20 bucks less than the version on the competitor"
Nope. They could do that and still make the same profit.... but they certainly wouldn't have to. They'd probably just continue selling at the same price and enjoy the extra profit they make instead of passing the savings onto consumers. That's what businesses usually do. I mean, just look at Steam! I think they charge 30%, yet despite console games having to pay console royalties and a % to retailers for physical copies too (which probably adds up to more than Steam alone charge), new games are often listed at a higher price on Steam than they are on console.