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arXiv:2602.17213

Extending quantum theory with AI-assisted deterministic game theory

Florian Pauschitz, Ben Moseley, Ghislain Fourny

quant-phcs.AIcs.GTSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations
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Abstract

We present an AI-assisted framework for predicting individual runs of complex quantum experiments, including contextuality and causality (adaptive measurements), within our long-term programme of discovering a local hidden-variable theory that extends quantum theory. In order to circumvent impossibility theorems, we replace the assumption of free choice (measurement independence and parameter independence) with a weaker, compatibilistic version called contingent free choice. Our framework is based on interpreting complex quantum experiments as a Chess-like game between observers and the universe, which is seen as an economic agent minimizing action. The game structures corresponding to generic experiments such as fixed-causal-order process matrices or causal contextuality scenarios, together with a deterministic non-Nashian resolution algorithm that abandons unilateral deviation assumptions (free choice) and assumes Perfect Prediction instead, were described in previous work. In this new research, we learn the reward functions of the game, which contain a hidden variable, using neural networks. The cost function is the Kullback-Leibler divergence between the frequency histograms obtained through many deterministic runs of the game and the predictions of the extended Born rule. Using our framework on the specific case of the EPR 2-2-2 experiment acts as a proof-of-concept and a toy local-realist hidden-variable model that non-Nashian quantum theory is a promising avenue towards a local hidden-variable theory. Our framework constitutes a solid foundation, which can be further expanded in order to fully discover a complete quantum theory.

Comments
Extended abstract, 3 pages plus references. Preprint in progress

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We present an AI-assisted framework for predicting individual runs of complex quantum experiments, including contextuality and causality (adaptive measurements), within our long-term programme of discovering a local hidden-variable theory that extends quantum theory. In order to circumvent impossibility theorems, we replace the assumption of free choice (measurement independence and parameter independence) with a weaker, compatibilistic version called contingent free choice.
Our framework is based on interpreting complex quantum experiments as a Chess-like game between observers and the universe, which is seen as an economic agent minimizing action. The game structures corresponding to generic experiments such as fixed-causal-order process matrices or causal contextuality scenarios, together with a deterministic non-Nashian resolution algorithm that abandons unilateral deviation assumptions (free choice) and assumes Perfect Prediction instead, were described in previous work.
In this new research, we learn the reward functions of the game, which contain a hidden variable, using neural networks. The cost function is the Kullback-Leibler divergence between the frequency histograms obtained through many deterministic runs of the game and the predictions of the extended Born rule.
Using our framework on the specific case of the EPR 2-2-2 experiment acts as a proof-of-concept and a toy local-realist hidden-variable model that non-Nashian quantum theory is a promising avenue towards a local hidden-variable theory. Our framework constitutes a solid foundation, which can be further expanded in order to fully discover a complete quantum theory.
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.
We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement scenarios are multiplayer games with a structure all observers agree on. Measurement axes and, newly, measurement outcomes are modeled as decisions with nature being an action-minimizing economic agent. We translate physical notions of causality, correlation, counterfactuals, and contextuality to particular aspects of game theory. We investigate the causal consistency of dynamic games with imperfect information from the quantum perspective and conclude that counterfactual dependencies should be distinguished from causation and correlation as a separate phenomenon of its own. Most significantly, we observe that game theory based on Nash equilibria stands in contradiction with a violation of Bell inequalities. Hence, we propose that quantum physics should be analyzed with non-Nashian game theory, the inner workings of which we demonstrate using our proposed model.
Abstract We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement scenarios are multiplayer games with a structure all observers agree on. Measurement axes and, newly, measurement outcomes are modeled as decisions with nature being an action-minimizing economic agent. We translate physical notions of causality, correlation, counterfactuals, and contextuality to particular aspects of game theory. We investigate the causal consistency of dynamic games with imperfect information from the quantum perspective and conclude that counterfactual dependencies should be distinguished from causation and correlation as a separate phenomenon of its own. Most significantly, we observe that game theory based on Nash equilibria stands in contradiction with a violation of Bell inequalities. Hence, we propose that quantum physics should be analyzed with non-Nashian game theory, the inner workings of which we demonstrate using our proposed model.
We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature (choice of outcomes). This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.
Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in an HVM means that the results of a measurement do not depend on settings for other measurements. If the measurements are spacelike separated, this assumption is known as local causality. Both free choice and CI mapping assumptions are considered necessary for derivation of the Bell-type criteria of contextuality/nonlocality. It is known, however, for a variety of special cases, that the two assumptions are not logically independent. We show here, in complete generality, for any system of random variables with or without disturbance/signaling, that an HVM that postulates CI mapping is equivalent to an HVM that postulates free choice. If one denies the possibility that a given empirical scenario can be described by an HVM in which measurements depend on other measurements' settings, free choice violations should be denied too, and vice versa. KEYWORDS: Contextuality; context-independent mapping; free choice; local causality; nonlocality.
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability measures over the continuous group SU(2) (mixed strategies). The Eisert-Wilkens-Lewenstein protocol is introduced as the standard implementation of quantum 2x2 games. We prove the existence of Nash equilibria for continuous quantum mixed strategies via a fixed-point argument, generalising the classical Nash theorem to the quantum case.