Gingrich has been an advocate of the long-form debate style, repeatedly saying on the campaign trail that if he were the Republican nominee, he would challenge President Obama to seven three-hour debates in the Lincoln-Douglas style and tradition. The debates would have no moderator, only a timekeeper.

The former House speaker has said that the debates offer the chance for a long-form discussion between candidates in which issues can be debated substantively. But the style also plays into his wheelhouse, favoring his professorial tone and deep policy background.

For Cain, the debate offers an opportunity to explain and defend his economic vision, which has come under attack recently as being regressive and likely to raise taxes all but the wealthiest Americans. The former pizza executive has complained that the current debate formats don't give him enough time to properly respond to critiques.

But the traditional debate style that Republicans have been using has also favored Cain in many ways, allowing him to employ pithy slogans and quick one-liners to great success. Polls show that his performance, especially contrasted to that of Texas Gov. Rick Perry, can help explain his rise in the GOP field.

No television network has yet signed on to televise the debate, which will be held at the Woodlands Resort near Houston.