A price war in the pizza business has convinced Yum Brands to throw in the towel. The corporate owner of the Pizza Hut chain is selling it to a private equity firm. Pizza Hut has struggled as consumers turn to the cheapest options for pizza delivery and other discretionary treats.Pizza Hut started out as a sit-down restaurant, as this 1990s commercial makes clear. But for pizza chains nowadays, in-house experiences are out, and cheap delivery is in. That transition has been tough for Pizza Hut, said Jonathan Maze, editor-in-chief of the trade publication Restaurant Business.“It's never really maintained its dominance as a pizza chain as a takeout and delivery concept,” he said.Higher gas prices and other inflation have consumers pulling back on pizza orders. And that’s a tough environment for Pizza Hut, according to Forrest Morgeson, who researches customer satisfaction and experience at Michigan State University. “I would say it's pretty clear to consumers that Domino’s and Little Caesars are the value way to go, whereas Pizza Hut is perceived as a little bit more of a higher-end pizza offering,” he said.And that perception could make turning Pizza Hut around quite a challenge.