Discover Financial Services is offering extra cardholder benefits for the holiday season in an attempt to win a bigger share of holiday spending.

Starting Nov. 15, Discover cardholders will earn double cashback bonus rewards of up to $1,000 on any online purchases they make through Dec. 31. Once they hit $1,000, cardholders still will earn 1% in cashback bonuses on all their purchases. They also will earn 5% in cashback bonuses on up to $300 in purchases at restaurants, department stores and clothing stores through December.

Ramping up deals on card rewards is all about driving use of Discover's card over rival brands, one analyst said.

"We're also talking about Discover here, [which] has lower market share" than other major card brands, said Ron Shevlin, an analyst at Aite Group in Boston. "So it's important for them to come out first and put the stake in the ground."

Discover also is expanding its redemption offers for the holidays, enabling cardholders to redeem cashback bonus rewards for bundles of consumer electronics. Shipping on purchased merchandise is free.

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