Updated

The 2012 WTA Championships commenced Tuesday when Agnieszka Radwanska beat reigning champion Petra Kvitova in round-robin action.

The fourth-seeded 2012 Wimbledon runner-up Radwanska whipped the sixth-seeded 2011 Wimbledon champion Kvitova, 6-3, 6-2, indoors at Sinan Erdem Arena.

Kvitova defeated current world No. 1 Victoria Azarenka in last year's final in Istanbul, which will also host this elite eight-player event next year.

Also on the Tuesday schedule, second-seeded Maria Sharapova will meet seventh- seeded Sara Errani and third-seeded Serena Williams is battling fifth-seeded Angelique Kerber. The former world No. 1 Sharapova bested Errani in the French Open final in June. The former top-ranked Williams was this year's Wimbledon, U.S. Open and Olympic champ.

Williams is a two-time WTA Championships titlist and two-time runner-up.

This week's four-player Group A features the current No. 1 and Australian Open champion Azarenka, Williams, Kerber and eighth-seeded Li Na, while Group B boasts the 2004 champion and 2007 WTA Championships runner-up Sharapova, Radwanska (1-0), Kvitova (0-1) and Errani.

The top two players in each group will advance to the semifinals and the winners will square off in the lucrative final on Sunday.

Azarenka needs only two wins this week to end the year at No. 1.

The winner of this $4.9 million season-ending event could collect as much as $1.75 million.