Steven R. Weisman on the history of the term:

[Joan] Robinson was apparently inspired by a card game popular in the 19th century, known as “Beggar-My-Neighbor.” One of the first literary appearances of the game was in the novel Great Expectations, published in 1861. Charles Dickens cited the game as the only one that Pip, the protagonist, seemed to know how to play. Hoyle’s says that “Beggar-My-Neighbor,” a kind of zero-sum game in which your opponent was not only defeated but left penniless, had such other names as “Beat Jack Out of Doors” and “Strip Jack Naked.”