The major credit card companies all covet the same customer segment these days — big spenders who pay off their entire bill each month, but still generate healthy profits because they swipe their plastic so often.

To woo these more affluent shoppers, American Express (AXP), Bank of America (BAC), Citigroup (NYSE: C), Capital One Financial (COF), Discover Financial (DFS) and JPMorgan Chase (JPM) are locked in an intense competition over card rewards.

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