Musical Games
Innis Xenakis was a music composer of the 20th century. His compositions were heavily based on mathematical principles. Two of his works, Duel and Strategie, were written based on Game Theory. Each piece is its own game and is written for two conductors—the players in the game. Specifically, Duel consists of six moves. These six moves are actually six different scores of music, one including silence. Of these six moves, silence is the worst move that a conductor can play. Each player conducts his orchestra in response to the other player’s move. Both players can read the game matrix before and during the game. The game can end after a certain number of moves, after a certain time limit has passed, or when a player reaches a winning score.
In the attached article, the authors describe an installation driven by software that mimics the game that Xenakis created in his composition Duel. For the program, a video camera will pick up the moves that the two players make. A motion of the arm in a certain direction signifies the choice of a certain move, 1 through 5. The sixth move (silence) does not have a movement associated with it. The players will always have visual access to the matrix, the score, time/moves remaining, and whose turn it is. The idea is that what the players hear and the movements he makes will be related. It can also be used for audience interaction. If the player chooses the right move, Xenakis observed that the audience clapped. The authors also mention extensions to this project like making it a man vs. computer game, allowing the composer to make his own matrix, and creating different sets of moves.
This article directly connects to class in that it is a clear application of Game Theory. The two conductors are the players, and different scores are the moves. Who would have thought we could find it in music? If you want to listen to pieces of the two compositions, here is the link: http://www.gametheory.net/popular/music.html. It’s the last listing on the page.
And here is the link to the paper: http://delivery.acm.org/10.1145/1140000/1133333/p322-liuni.pdf?ip=128.84.220.216&CFID=43569505&CFTOKEN=49286826&__acm__=1316484538_2a70baf768893634c2fcf7f19d46d115