I don't think this time they will. AMD introducing Big Navi and isn't Intel about to reveal their own graphics cards?
Will be a very competitive market soon
You say that, but AMD don't majorly force a pricing issue for Nvidia. They maybe undercut them by $50, but they'll want to cash in on the high price market. 5700 and XT didn't exactly force a price war, they just slotted into the gaps as they always do. In a VASTLY over simplified way, the price and performance of the cards always form pretty neet steps of $50-100.
$100 AMD 6500 10fps
$150 Nvidia 3050 15fps
$200 AMD 6600 20fps
$250 Nvidia 3060 25fps
There may be movements in pricing as each card launches and the others will adjust accordingly, but any real price war just doesn't exist.
There were rumours the 3950X would be the same price as a 9900k and Intel would have to adjust its pricing, but AMD aren't stupid, they know what their product is worth and what the market is willing to pay. They will follow whatever their competitors are doing, while doing just enough to ensure price fixing doesn't become a threat.