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Amazon and Whole Foods control only a sliver of the grocery market — for now

All bets are on Amazon to dominate the future of the grocery business, as it presses further into the category with its $13.7 billion deal for Whole Foods.

However, it will have a long way to go to gain the heft of other grocery players.

Wal-Mart Stores has the biggest share of the market, with about 14.5 percent of all U.S. food and grocery sales, according to estimates and analysis from GlobalData Retail.

Kroger is next with a 7.2 percent stake. After that, the market shares become smaller and more fragmented with Albertsons controlling 4.5 percent share, and Southeastern Grocers, the owner of the Bi-Lo, Harveys and Winn-Dixie brands, next with a 3.9 percent stake.

But Whole Foods and Amazon are smaller still, with Whole Foods controlling a 1.2 percent stake and Amazon with a 0.2 percent share.

But the combined company is widely expected to have an outsized influence over the market, boosting competition, particularly for organic and better-for-you foods.

"We anticipate Amazon's ownership is likely to result in lower prices at Whole Foods, forcing other grocery participants to follow, negatively impacting category margins," said Mark Astrachan, a Stifel analyst. "This could further accelerate the existing price war in retail."

He expects Wal-Mart to lead the price cuts in an effort to protect its share, but Amazon isn't likely to back off.

"We ... note Amazon has largely foregone profits in other categories in which it competes," Astrachan said.

— CNBC's Sarah Whitten contributed to this report.