The Bennet family makes up most of the core characters in Jane Austen's "Pride and Prejudice." It consists of Mr. Bennet, a father who wishes to remain uninvolved, Mrs. Bennet, a tiresome and interfering woman, and their five children. The five children are all daughters. Jane Bennet is the eldest daughter with Elizabeth Bennet, the main character, following her. Their three younger sisters from oldest to youngest are Mary, Kitty and Lydia.
The sibling rivalry to be found in "Pride and Prejudice" is nearly always, if not always, perpetuated by the silly and annoying Kitty and Lydia. Jane is a sweetheart who gets along with everybody. Elizabeth is mostly just aggravated and ashamed of her two youngest sisters. She gets along with the other two and has no rivalries. No one sees poor Mary as competition.
Kitty and Lydia are very similar in both age and temperament. This not only makes them close, but it makes them vie for the same things. On at least one occasion, Kitty complains that her sister gets to leave town when she does not. Lydia, who is a careless braggart, seems not to care, despite her seeming closeness with her sister.
A common theme throughout the novel is marriage. Mrs. Bennet is obsessed with marrying off her daughters. Her older three daughters do not seem to dwell on the idea much (until the two eldest Miss Bennets fall in love). However, the two youngest Miss Bennets can think of little else. They want to flirt with officers, meet rich men, fall in love with one and get married. They are so open and obvious about their shallow desires that Elizabeth is quite embarrassed by them. Furthermore, they seem to be in a competition, in their own minds, to marry first. It is not said outright. However, after a botched and shameful marriage for Lydia, she brags to her sisters about how she was the first to marry.
Lydia is by far the worst when it comes to petty competition with her sister. Competitions that she seems to be the only one interested in, it is worth noting. However, Kitty and Mary are not exempt from sibling rivalry. Their incidences of it are simply on a much smaller scale. For Kitty, her rivalry tends to start and end with Lydia. Mary tries very hard to be a voice of reason (a somewhat dull one, at that) when her sisters are being ridiculous. It sometimes appears as if this is how she seeks to divert attention away from her sisters. She never prevails.
There are a few other sets of siblings in Pride and Prejudice, but no other sibling rivalry to speak of. Mr. Darcy gets along wonderfully with his sister, Georgiana. Mr. Bingley has a horribly shallow and scheming sister, but she does not appear to be in competition with him over anything, unless you include Mr. Darcy's attention.