A price war is a situation that frequently occurs in an oligopolistic business market when companies begin to aggressively lower their prices to compete with each other, which can cause some pretty interesting price combinations for consumers (like $9 airline tickets).
A Primer on Oligopoly
An oligopoly is a market setup in which there are a few very powerful firms that collectively control most of the product being exchanged in the market. Examples include OPEC, the airline industry, and ye olde broadcast television industry. Because there are only a few powerful firms in the market, they can have a direct impact on the price of goods, unlike in a perfectly competitive market, where the producers all charge basically the same price (think foodstuff markets).
Because of the substantial price-setting power possessed by these firms, each of them has an incentive to drop its prices and capture a larger section of the market. By doing so, they can get a large amount of money from their customers, and hopefully starve one of their competitors to death. This happens because all oligopolists really want to be monopolists, so they are constantly trying to kill off their competition.
Gentlemen, draw your swords!
When one of the companies decides to drop its price, all of its competitors must immediately drop their own prices as well, or risk losing business. This would be simple, except that most of the time, these companies drop their prices lower than the first guy. Now you have a price war.
All of the companies continue undercutting each other until some event causes them to reevaluate their collective sanities, and they give up, returning prices usually to about the same as they were before the war. Remember kids: the best time to be a consumer is during a price war; the worst time to be a producer is during a price war.
Price wars usually begin because of an especially lucrative business opportunity: the CEO of a rival calls it quits, putting its leadership off-balance; a holiday season begins; vacation seasons begin or end; some strange geopolitical rumbling changes the game ever so slightly, etc. They tend to not last very long, because companies very quickly find themselves selling product at huge losses (again, $9 flights). The conclusion of a price war usually occurs when either the season that started it ends or one of the competitors goes out of business. Usually the latter is a big red flag to the companies, and they throttle back their price cuts and everybody can start breathing easier.