Contingent Free Choice: On Extending Quantum Theory to a Contextual, Deterministic Theory With Improved Predictive Power
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The non-extensibility of quantum theory into an extended 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. However, an alternate line of game-theoretical research based on the weaker assumption of contingent free choice, leads to non-trivial solution concepts with desirable properties such as at-most uniqueness, Pareto optimality, as well contextuality. We show how introducing contingent free choice in the foundations of quantum theory yields a class of deterministic, contextual and non-trivial theories with an improved predictive power, and contrast it with the pilot-wave theory. Specifically, we suggest that quantum experiments, such as the EPR experiment, involving measurements across positions in spacetime, can be recast as a game with imperfect information between human agents and the universe. The suggested 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 such game based on strong free choice is put in perspective with local hidden variable theories, constrained by the Bell inequalities. On the other hand, in a setup in which agents are rational in all possible worlds and epistemically omniscient, under contingent free choice, the Perfectly Transparent Equilibrium provides a contextual resolution towards an at-most unique possible world, in which the outcomes of measurements that actually are carried out, and only them, are deterministically defined.
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