A Note on Weakening Free Choice in Quantum Theory

The non-extensibility of quantum theory into a non-trivial, noncontextual deterministic theory is based on a strong assumption of free choice, in which the physicists pick a measurement axis independently of the rest of the world. This same strong assumption of free choice is at the core of Nashian game theory. However, recent game-theoretical research based on a weakened version of free choice lead to non-trivial solution concepts with desirable properties. In this note, we share our view that a similar change of assumption to the modelling of free choice in the foundations of quantum theory opens a non-trivial avenue of research towards a deterministic and non-trivial version of quantum theory with, at least in theory, an improved predictive power. At this point, this note is a draft that will be regularly updated and completed based on feedback and discussions