Overstock announced today that they were extending their sale. The deep discounted prices are going to stay in effect at least through 7 August, and possibly even later. The CEO told PW that he plans to review the situation in a week and consider the matter then.
There's no word yet on how Amazon plans to respond, though I would not be surprised if they also continued to offer the deep discounts on best sellers. Amazon has always had a policy of matching competitor's (most of the time), and they've never been one to step away from a fight.
That is certainly one way to describe the last time Amazon got into a price war over books. Back in 2009 Amazon, Walmart, and Target got into a 3 way tussle over new best sellers (followed by another war over DVDs). That war was started by Walmart, which first announced that they would sell 10 new hardcover titles at $9.99. After Amazon (and later Target) matched the price, Walmart lowered their prices again.
I have no direct info on how long that war lasted, but I am told that the 3 retailers went through several rounds of price cuts before someone blinked. There is a good chance that the same thing could happen in the Overstock/Amazon price war.