It will ratchet downward because the competitor wants to maximize his revenue. This is because the competitor knows that if he lowers his price incrementally (say 1%), he will sell more products (2% more products, for example). The end result is more revenue for the competitor. This is exactly the invisible hand that regulates prices. Of course, this whole scheme breaks down if there is a "trust" or agreement between the two companys...but that would be illegal. I am not a economist, mind you.
In some markets, that may be true, in others not -- it depends on market elasticity. If he has to drop the price 20% to get 10% more volume, guess what a rational businessman is going to do?