By Jessica Shambora, reporter

Kahn Lucas vs. American Girl

The challenge: More than 18 million American Girl dolls have been sold since being introduced in 1986. Is there room for another “dress like your doll” company?

What they did: Kahn Lucas, a 121-year-old girls’ apparel company in Lancaster, Pa., last year launched a new line called Dollie & Me, which, like American Girl, lets little girls wear outfits that match those of their dolls. But rather than trying to break into the entrenched doll market, Kahn Lucas partners with Madame Alexander, a dollmaker. Unlike American Girl, which sells only through its flagship stores and online, Kahn Lucas also taps into existing relationships with retailers like Sears (SHLD), Kohl’s (KSS), and Amazon.com (AMZN). Dollie & Me dolls and clothes are also priced lower. The company expects to see 400% revenue growth for Dollie & Me this year, along with 800 new outlets.

Rudy’s Music vs. Guitar Center

The challenge: Rudy’s, with two shops in New York City, faces off against Guitar Center, with 214 locations nationwide. A case study in independent-retailer survival.

What they did: Specialize! Guitar Center cuts costs by buying in bulk, but it doesn’t have the cachet of Rudy’s, which is part guitar shop, part landmark, thanks to clients like Lou Reed and Eric Clapton. Since opening his first store in midtown Manhattan in 1978, Buenos Aires-born Rudy Pensa has stocked high-end niche guitars and amps like Froggy Bottom and Blankenship. He also carries vintage instruments, some previously owned by famous musicians, as well as his own line of Pensa guitars, designed with Mark Knopfler of Dire Straits fame. If you buy from Rudy’s, you’re a customer for life, meaning special care at his repair shop, where bands like U2 and Metallica go for tune-ups.

Popchips vs. Frito-Lay

The challenge: Frito-Lay  has nearly 60% of the potato chip market and has dominated the healthy-chip segment since introducing Baked Lays in 1996.

What they did: Popchips began its campaign to upend the snack aisle in 2007. Co-founder pals Keith Belling and Pat Turpin created a cross between a potato chip and a rice cake by, well, popping potatoes like popcorn. Because no oil is used in the popping process, Popchips have fewer calories and less than half the fat of fried potato chips. The great taste and health factor have attracted investors like actor Ashton Kutcher and turned fans into vocal evangelists. Popchips also distributes through outlets with cult followings of their own, like Jamba Juice and Whole Foods (WFMI). How’s business? Popchips expects to grow another 200% this year, with sales exceeding $40 million.