The Nash Equilibrium of Jazz: Why Musicians “Defect” to Free Jazz in Non-Cooperative Games

The “Rational” Jam Session

As the winter winds batter the windows of 7 Inverlochy Place, inside the warmth of the recital hall, the Department of Economics is attempting to quantify the unquantifiable: the mathematics of “cool.”

To kick off the Semester 2 Winter Lecture Series, Dr. Percival Thorne (Economics) teamed up with jazz instructor Mr. Tane Heke to present a provocative experiment titled “Rationality in Rhythm: Modelling Improvisation as a Non-Cooperative Game.”

The premise was derived from classical Game Theory. Two student musicians—a pianist and a saxophonist—were placed on stage. They were given a simple chord progression and a strict set of rules. For every 16 bars, they had to choose a strategy:

1. Cooperate: Play supportive, harmonic accompaniment (low ego, high stability).
2. Defect: Play a complex, high-volume solo (high ego, high risk).

The Payoff Matrix

The students were hooked up to biometric monitors, and the audience’s applause was measured by precise decibel meters after each round to determine the “Utility Payoff.”

The theoretical model, projected on the screen behind the musicians, predicted a classic “Prisoner’s Dilemma”:

• If both Cooperate, the music is pleasant but boring (Medium Payoff).
• If one Defects (solos) and the other Cooperates (comps), the soloist gets the glory (High Payoff) and the accompanist gets ignored (Low Payoff).
• If both Defect (solo simultaneously), the result should be cacophony (Negative Payoff/Crash).

“Mathematically,” Dr. Thorne explained to the packed hall, “the Nash Equilibrium suggests that rational actors will eventually gravitate towards a state where no one can improve their position by deviating. In music, this should result in a polite, balanced exchange of solos.”

The “Free Jazz” Anomaly

However, human creativity proved to be a stubborn variable. As the experiment progressed into the fourth round, both students chose to “Defect” simultaneously. Instead of backing down to restore harmony, the pianist began hammering dissonant clusters while the saxophonist screamed in the altissimo register.

According to the model, the audience reaction should have plummeted. The algorithm flagged this state as “Market Failure” (Total Dissonance).

Yet, the decibel meters told a different story. The audience erupted in the loudest applause of the night.

“The model failed because it assumed the audience demanded order,” admitted Mr. Heke during the post-concert critique. “It didn’t account for the ‘Avant-Garde Multiplier.’ In jazz, total chaos isn’t necessarily a negative outcome; if framed correctly, it’s art. The economists treated dissonance as a cost, but the musicians successfully sold it as an asset.”

The Ego Premium

Further analysis of the students’ individual choices revealed an interesting psychological trend. Even when the “Cooperate” strategy offered a guaranteed, safe reward (polite applause), the musicians consistently chose to “Defect” more often than probability would suggest.

Ms. Yuna Kim from the Econometrics department termed this the “Ego Premium.”

“The students derived utility not just from the external reward (applause), but from the internal satisfaction of virtuosity,” Ms. Kim noted in her summary report. “They were willing to risk wrecking the performance for the chance to play a diminished-scale run. It suggests that in creative industries, actors are inherently risk-seeking, which makes standard predictive models unreliable.”

Refining the Model

The experiment concluded with a humbling realization for the quantitative analysts. The “Prisoner’s Dilemma” assumes that the prisoners want to minimize jail time. Musicians, it turns out, don’t mind going to jail as long as they get to play a famous solo on the way there.

The faculty plans to rerun the experiment later in the term, introducing a “Conductor” variable to act as a central regulator, essentially imposing a “tax” on excessive soloing to see if it forces a return to equilibrium.

For now, the lesson for our economics students is clear: rationality is a powerful tool, but it struggles to account for the improvisational spirit of the human ego.