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 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 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.
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.
Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as general communication equilibria, belief-invariant equilibria and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium has appeared in game theory before, in the 1990s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 1980s in the foundations of quantum mechanics.
In the present work, we explain and unify these two origins of the idea and study the above classes of equilibria, and furthermore quantum correlated equilibria, using tools from quantum information but the language of game theory. We present a general framework of belief-invariant communication equilibria, which contains (quantum) correlated equilibria as special cases. Our framework also contains the theory of Bell inequalities, a question of intense interest in quantum mechanics and the original motivation for the above-mentioned studies.
We then use our framework to show new results related to social welfare. Namely, we exhibit a game where belief-invariance is socially better than correlated equilibria, and one where all non-belief-invariant equilibria are socially suboptimal. Then, we show that in some cases optimal social welfare is achieved by quantum correlations, which do not need an informed mediator to be implemented. Furthermore, we illustrate potential practical applications: for instance, situations where competing companies can correlate without exposing their trade secrets, or where privacy-preserving advice reduces congestion in a network. Along the way, we highlight open questions on the interplay between quantum information, cryptography, and game theory.
A probabilistic framework is developed that gives a unifying perspective on both the classical and quantum versions of two-player games. We suggest exploiting peculiar joint probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct a quantum game when the corresponding classical game is obtained from factorizable joint probabilities. We analyze how nonfactorizability changes Nash equilibria in three well-known games of prisoner's dilemma, stag hunt, and chicken. In this framework we find that for the game of prisoner's dilemma even nonfactorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the chicken game, however, we find that the two nonfactorizable sets of joint probabilities, which maximally violate the Clauser-Holt-Shimony-Horne sum of correlations, indeed result in new Nash equilibria.