The New York Times gives notice of Michael Chwe, Jane Austen, Game Theorist, just published by Princeton University Press. Chwe is a stellar young economist whose 2001 Rational Ritual: Culture, Coordination, and Common Knowledge is fascinating, though a bit technical. A couple years ago Chwe published "Rational Choice and the Humanities: Excerpts and Folktales" in Occasion, which is available online, and in which he discusses examples from Shakespeare and Richard Wright before moving on to folktales, which also get a chapter in the Austen book.
From the NYTimes article, after noting that game theory was invented by John von Neumann in the 1940s and quickly became a staple of Cold War strategic analysis and in several academic disciplines, including economics and biology:
Take the scene in “Pride and Prejudice” where Lady Catherine de Bourgh demands that Elizabeth Bennet promise not to marry Mr. Darcy. Elizabeth refuses to promise, and Lady Catherine repeats this to Mr. Darcy as an example of her insolence — not realizing that she is helping Elizabeth indirectly signal to Mr. Darcy that she is still interested.
It’s a classic case of cluelessness, which is distinct from garden-variety stupidity, Mr. Chwe argues. “Lady Catherine doesn’t even think that Elizabeth” — her social inferior — “could be manipulating her,” he said. (Ditto for Mr. Darcy: gender differences can also “cause cluelessness,” he noted, though Austen was generally more tolerant of the male variety.)
I've not read the Austen book, but I do have one misgiving. Game theory is about interactions between autonomous individuals. While novels depict their characters as being autonomous actors, they are not autonomous. They are creatures of the author.