From the Selector Infected WIXOSS Wikia:

This story revolves around two pairs of Selectors and their LRIGs: Yuragi and Alfou as well as Mako and Haiti.

From Wikipedia (the anime's story and general background for the two manga):

WIXOSS (short for "Wish Across") is a popular trading card game in which players battle against each other with fighters known as LRIGs (girl spelled backwards; pronounced Rurigu), using cards to support them.

Ruko Kominato, who receives a WIXOSS deck from her brother, discovers that her LRIG, which she names Tama, can speak. She soon learns that she has been chosen as a 'Selector', girls who must battle against other Selectors. Should they be victorious in battle, they will be able to have any wish granted, but should they lose three times to other Selectors, they will lose that chance and lose all memory of the game.

As she and various other Selectors battle it out for the sake of their wish, Ruko finds herself drawn into the dark sinister world of WIXOSS, discovering that win or lose, there is always a cost.