“There are at least two kinds of games,” states James P. Carse as he begins this extraordinary book. “One could be called finite; the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.”

Finite games are the familiar contests of everyday life; they are played in order to be won, which is when they end. But infinite games are more mysterious. Their object is not winning, but ensuring the con...