# Contingent Free Choice: On Extending Quantum Theory to a Contextual, Deterministic Theory With Improved Predictive Power

## TL;DR

This paper proposes a new deterministic, contextual extension of quantum theory by relaxing free choice assumptions, framing quantum experiments as dynamic games with imperfect information involving human agents and the universe.

## Contribution

It introduces contingent free choice into quantum foundations, leading to a class of theories with improved predictive power and a novel game-theoretic interpretation of quantum experiments.

## Key findings

- Contingent free choice yields deterministic, contextual theories.
- Quantum experiments can be modeled as dynamic games with imperfect information.
- The approach offers a resolution similar to the Perfectly Transparent Equilibrium.

## Abstract

The non-extensibility of quantum theory into a theory with improved predictive power is based on a strong assumption of independent free choice, in which the physicists pick a measurement axis independently of anything that couldn't have been caused by their decision. Independent free choice is also at the core of the Nash equilibrium and classical game theory. A more recent line of game-theoretical research based on weakening free choice leads to non-trivial solution concepts with desirable properties such as at-most uniqueness, Pareto optimality, and contextuality. We show how introducing contingent free choice in the foundations of quantum theory yields a class of deterministic and contextual theories with an improved predictive power, and contrast them with the pilot-wave theory. Specifically, we suggest that quantum experiments, such as the EPR experiment, involving measurements located in spacetime, can be recast as dynamic games with imperfect information involving human agents and the universe. The underlying idea is that a physicist picking a measurement axis and the universe picking a measurement outcome are two faces of the same physical contingency phenomenon. The classical, Nashian resolution of these games based on independent free choice is analogous to local hidden variable theories, constrained by the Bell inequalities. On the other hand, in a setup in which agents are rational and omniscient in all possible worlds, under contingent free choice, the Perfectly Transparent Equilibrium provides a contextual resolution, based on the iterated elimination of inconsistent worlds, towards an at-most unique possible world, in which the outcomes of measurements that actually are carried out, and only them, are deterministically defined.