Free Jazz Improvisation and Game Theory
Could game theory help us produce music in an improvisational setting? How about helping us think about free improvisational music?
Iannis Xenakis proposes a game that falls more into the former category: Duel is a piece for two orchestras with 2 conductors where each conductor has a set of musical strategies. There is a matrix given with the musical score (sheet music) for the payoffs of each strategy in relation to what the other orchestra does. If there were only two strategies (silence or playing long notes), the matrix would be something like this:
Orchestra 2
A (silence) B (long notes)
A -5,-5 0, +5
Orchestra 1
B +5,0 +3,+3
This is a very simple example, but the game gets far more complex when there are more possible strategies.
Would this work for free jazz improvisation? We see that Xenakis’ approach is prescriptive; that is, the matrix tells the players what they should do. In addition, the game is agonistic, as the players function as opponents. If we were to remove the musical score (as one does in jazz), the only given material would be the matrix. The major problem here is that the matrix itself would act similarly to a score by prescribing a set of rules, so we find that we can’t use game theory to make truly free improvisation after all.
Instead, maybe we can use it to think about free improvisation. We can think about free improv as a pure coordination game, where all musicians must be on the same page with each other (chordal/harmonic changes, tempo, etc.). Though at first it might seem purely speculative to think about free improv as a pure coordination game (musicians can’t all have the same preferences about everything!), we can toss aside the individualistic aspect of game theory and instead consider the musicians playing together to be a team, where the musicians not only have a common goal but also common interests. So, while we have seen that game theory might not be used as a tool to make improvisational music, it might function as an interesting descriptive tool!