This delightful site lists and describes the uses of game theory in film, television, music and other areas of popular culture. The entry for Dr. Strangelove, for instance, reads as follows:
Kubrick’s cold war dark comedy. One five-minute scene explains credible commitment, highlighting the importance of clarity, irreversibility, and public knowledge.
Maybe you already knew that one, but check out the takes on House of Games, Princess Bride, and War Games, all underrated movies, chock full of game theory. See also the site’s treatment of TV shows, the links on music and books are skimpier and less convincing. The book section could be much more complete, the music section is doomed to be short, at least they could have mentioned John Cage’s idea for “aleatory” (random) composition. We do learn that the Greek composer Xenakis once wrote an intentionally game-theoretic piece for two competing orchestras.