Nashian game theory is incompatible with quantum physics

IF 0.9 Q3 PHYSICS, MULTIDISCIPLINARY
Michal Baczyk, Ghislain Fourny
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引用次数: 1

Abstract

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.
纳什博弈论与量子物理学不相容
我们建议通过决策理论而不是概率论的视角来看待量子测量结果。我们引入了一个原始的游戏理论框架、模型和算法程序,其中测量场景是具有所有观察者都同意的结构的多人游戏。测量轴和新的测量结果被建模为决策,自然是一个行动最小化的经济主体。我们将因果关系,相关性,反事实和情境性的物理概念转化为博弈论的特定方面。我们从量子的角度研究了不完全信息动态博弈的因果一致性,并得出结论,反事实依赖应该与因果关系和相关性区分开来,作为一个独立的现象。最重要的是,我们观察到基于纳什均衡的博弈论与违反贝尔不等式是矛盾的。因此,我们建议量子物理学应该用非纳什博弈论来分析,我们使用我们提出的模型来演示其内部工作原理。
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来源期刊
Quantum Studies-Mathematics and Foundations
Quantum Studies-Mathematics and Foundations PHYSICS, MULTIDISCIPLINARY-
CiteScore
2.10
自引率
12.50%
发文量
21
期刊介绍: The primary goals of Quantum Studies: Mathematics and Foundations are to promote a deeper understanding of all fundamental aspects of quantum theory and to bridge between theoretical questions, foundational issues, mathematical methods, and the further evolution of quantum physics. Papers of high scientific quality in and between these domains are welcome. The emphasis is on mathematical methods and insights that lead to a better understanding of the paradoxical aspects of quantum physics and to its expansion into new domains. We encourage the creative use of such paradoxes and invite research articles and surveys. The target audience of this international journal are physicists, mathematicians and philosophers of science with an interest in the fundamental aspects of quantum theory.
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