  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.
