This isn't uncharted territory. Pricing for duopolies vs monopolies have been well-studied and well-characterized.
Intel doesn't have to respond with their Kaby Lake processors, since at the moment AMD hasn't released equivalent competitors. Prices should (and have) drift slightly lower but not much will happen until AMD releases the lower end chips. For example, the 7700K dropped $6.67 on Amazon today.
With HEDT, I'll just go with simple duopoly pricing models. Take the 6800K for example. In a monopoly, no one would pay more than $617 for the 6800K, since they can buy the better 6850K for that price. Also, lets assume these HEDT chips cost Intel more to manufacture than typical consumer chips. I'll guess $100 just for a round number. In a monopoly, the maximum profit occurs roughly 2/3rds of the way from the cost to produce and the maximum price that anyone would pay. Thus, in a monopoly, to maximize profit, the 6800K should be priced at ($617*2 + $100) / 3 = $444. That isn't too far off from the $434 release price.
But in a duopoly, the maximum profit occurs at a lower point. Typically that maximum profit comes in right around the average of (A) the maximum price that anyone logical would pay and (B) the cost to produce the item. In this case, I would say the maximum anyone would pay for the 6800K is the $499 price of the better Ryzen 1800X. Thus, the 6800K would generate maximum profit at a price of about ($499 + $100) / 2 = $299. Intel should thus lower the 6800K price by about $135 if they want to maximize profit. That pits it right up against the $329 Ryzen 1700, which would be close competition.
That is a 31% price drop after being in the field for 9 months. Investors wouldn't blink an eye at that small of a price drop in a technology field (and a very small subset of Intel's products). Intel doesn't have to drop prices, or they could drop prices more than 31%. But, 31% is roughly what Intel should do for the 6800K.
The 6900K can be analyzed similarly, although there isn't as clear of a top price that anyone would pay since there isn't a good comparable chip. I'd expect closer to a 35% drop, to somewhere in the $700 range for the 6900K to maximize profits. Again, Intel doesn't have to respond, but the proper response would be to cut the 6900K to roughly $700.