Could "against" be replaced by "by" in this phrase?

"By" would affect the intent of the statement. When two people or groups are "being played off against each other" there is an implied 3rd party involved and that the two groups are competeing for something the 3rd party has.

If it is changed to "being played off by each other" then it implies that the only "players" are the two groups themselves.

"Played off" doesn't mean being defeated. It means that the two are competing for something. Usually the "winner" in such events is the 3rd party. An auction is a good example. Instead of bidding (competing) against the seller you are bidding against other people that also want the item up for sale. The seller isn't driving the price up. The bidders do that themselves. The seller ends up the winner as the price climbs higher. In any auction the seller is "playing off one bidder against another".

Thank you fishin' ...It made me get to know the difference.

Thank you yitwail It lit up a bulb in my brain.

Heh, wow. I just have to comment on this thread--I've read a few and am amazed at how great the detail is of information. I'm almost looking forward to the next grammatical question I have now that I know where to bring it!