Pizza wars have broken out, as Pizza Hut and Papa John's start the new year with new low-priced offers for their pizza.

Pizza Hut, the world's largest pizza chain, is offering customers the chance to buy a medium pizza with one topping for $5 as long they buy at least one other item such as breadsticks, soft drinks, wings or a second pizza also for $5. The offer started Monday.

Papa John's is offering customers who buy a large pizza at regular price the chance to buy a second for only 50 cents.

Pizza Hut, a unit of Yum Brands (YUM), has reported essentially flat sales at its U.S. stores through the first three quarters of 2015. That is well behind the 5% growth reported by Papa John's (PZZA) at its North American stores, and the 13% revenue growth at domestic stores of No. 2 pizza chain Domino's (DPZ).

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The Pizza Hut offer is similar to a $5.99 offer that Domino's has been offering in one form or the other since 2010.

"We don't play the price or product-of-the-month gimmick game others seem to. The limited-time-only tactic is something we left behind years ago," said Domino's spokesman Tim McIntyre. He said Domino's is the only national pizza chain that has been able to achieve sales growth every year since 2009.