Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

The quantum foundations of utility and value

Cal Abel

Published Jun 19, 2023• 8 citations
Publisher

Abstract

This work presents a generalization of game theory and new perspectives on utility and value. Using quantum formalism, we prove that classical game theory is a special case of quantum game theory. We show that the von Neumann entropy and von Neumann-Morgenstern utility are equivalent and that the Hamiltonian operator represents value. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

DOI
10.1098/rsta.2022.0286

Related papers

Quantum Game Theory

Huilin Zhao

Since the establishment of von Neumann and Nash's concept of equilibrium, game theory has become a universal language in economics and social sciences. However, classical game theory is deeply rooted in the mechanistic worldview, and its deterministic assumptions, static equilibrium, and individualistic methodology are becoming increasingly inadequate in explaining the emergence of cooperation, uncertainty, and complex social interactions. This book directly faces this dilemma and introduces the core concepts of quantum mechanics into game analysis, constructing a complete system of quantum game theory. Starting from the century long evolution of game theory, the entire book deeply criticizes the mechanistic nature of classical game theory, and re establishes the philosophical foundation of game theory through practical ontology. On this basis, this book proposes the hypothesis of a "quantum gamer" and constructs a complete analytical framework from superposition strategy space, quantum entanglement to measurement collapse. The system reconstructs core areas such as quantum zero sum games, quantum non-zero sum games, quantum prisoner's dilemma, quantum coordination games, quantum evolutionary games, quantum cooperative games, and quantum incomplete information games, and extends them to cutting-edge directions such as quantum repetitive games, quantum game learning, and quantum mechanism design. At the application level, this book comprehensively demonstrates the broad prospects of quantum game theory in fields such as economics, political science, sociology, biology, computer science, quantum computing, artificial intelligence, and ethics. This book emphasizes that quantum entanglement enables cooperation to emerge, and quantum measurement leads equilibrium from static to dynamic collapse, thus surpassing the explanatory boundaries of classical game theory. The book has a rigorous structure and in-depth arguments, combining theoretical originality with interdisciplinary perspectives, providing a groundbreaking work for researchers, graduate students, and cutting-edge explorers to understand the quantum game revolution.

•Sep 3, 2026•0 citations

Quantum and classical approaches in statistical physics: some basic inequalities and game theoretic interpretation

Lev Sakhnovich

We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. The extremal principles (e.g., the Fermat's principle of least time and the least action principle), which remain central in modern physics, are formulated in terms of one physical value. Using our inequalities, we give a game theoretic interpretation of the interaction of three physical values, namely, free energy, entropy and mean energy. Such approach is inspired by Neumann--Morgenstern and Nash game theories. According to these game theories, the transition from the deterministic strategy (classical mechanics) to probabilistic strategy (quantum mechanics) increases the winning for all players. In the second part of the paper, we simultaneously derive the quasi-classical limits for four cases, that is, for $h{\to}0$, $T{\to}\infty$, $\omega{\to}0$, and $N{\to}\infty,$ where $h$ is the Planck constant, $T$ is the absolute temperature, $\omega$ is the frequency of an oscillator, and $N$ is the degree of freedom of a system. We note that only the first case is usually considered in quantum physics. The second case was studied initially by M. Planck and the third case by A.~Einstein.

•Jun 19, 2020•0 citations

Quantum Games, Quantum States, Their Properties and Applications

Dmitrijs Kravcenko

Quantum mechanics and game theory were developed at almost the same time, during the first half of 20th century.Classical game theory is one of the most developed in mathematics and computer science.It has many applications in economics, biology, and different kinds of social science.In computer science, many cryptographic protocols are also based on the elements of game theory.Quantum computing is a relatively new branch of computer science.It unites different aspects of complexity theory and quantum physics.Our intention is to take it one step further and combine classical game theory with the acquired knowledge of quantum computing; in particular, to study the effects of using quantum information in the well-known problems of game theory.In this thesis, we obtain several bounds on the values of some special classes of nonlocal quantum games, and we present a new scheme for games quantization.

•Jan 1, 2013•0 citations

John von Neumann between Physics and Economics: A Methodological Note

Luca Lambertini

A methodological discussion is proposed, aiming at illustrating an analogy between game theory in particular (and mathematical economics in general) and quantum mechanics. This analogy relies on the equivalence of the two fundamental operators employed in the two fields, namely, the expected value in economics and the density matrix in quantum physics. I conjecture that this coincidence can be traced back to the contributions of von Neumann in both disciplines.

Review of Economic Analysis•Jul 1, 2013•3 citations

Quantum and classical approaches in statistical physics: game theoretic interpretation

Lev Sakhnovich

The extremal principles, for instance, the Fermat's principle of least time and the principle of least action remain central in modern physics. The named above extremal principles are formulated in terms of one physical value. In the present paper, we give the game theoretic interpretation of the interaction of the three physical values: mean energy E, entropy S and free energy F. Such approach is inspired by the Neumann--Morgenstern game theory and the Nash game theory. According to these game theories, the transition from the deterministic strategy to probabilistic strategy increases the winning for all players. From this point of view we consider the connection between classical mechanics (deterministic strategy) and quantum mechanics (probabilistic strategy). In the present paper, we improve, develop and generalize our previous results.

•Jun 19, 2020•0 citations

Introduction to the study of entropy in Quantum Games

Esteban Guevara Hidalgo

The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.

arXiv:quant-ph/0604170•Apr 24, 2006•5 citations
This work presents a generalization of game theory and new perspectives on utility and value. Using quantum formalism, we prove that classical game theory is a special case of quantum game theory. We show that the von Neumann entropy and von Neumann-Morgenstern utility are equivalent and that the Hamiltonian operator represents value. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.
Since the establishment of von Neumann and Nash's concept of equilibrium, game theory has become a universal language in economics and social sciences. However, classical game theory is deeply rooted in the mechanistic worldview, and its deterministic assumptions, static equilibrium, and individualistic methodology are becoming increasingly inadequate in explaining the emergence of cooperation, uncertainty, and complex social interactions. This book directly faces this dilemma and introduces the core concepts of quantum mechanics into game analysis, constructing a complete system of quantum game theory. Starting from the century long evolution of game theory, the entire book deeply criticizes the mechanistic nature of classical game theory, and re establishes the philosophical foundation of game theory through practical ontology. On this basis, this book proposes the hypothesis of a "quantum gamer" and constructs a complete analytical framework from superposition strategy space, quantum entanglement to measurement collapse. The system reconstructs core areas such as quantum zero sum games, quantum non-zero sum games, quantum prisoner's dilemma, quantum coordination games, quantum evolutionary games, quantum cooperative games, and quantum incomplete information games, and extends them to cutting-edge directions such as quantum repetitive games, quantum game learning, and quantum mechanism design. At the application level, this book comprehensively demonstrates the broad prospects of quantum game theory in fields such as economics, political science, sociology, biology, computer science, quantum computing, artificial intelligence, and ethics. This book emphasizes that quantum entanglement enables cooperation to emerge, and quantum measurement leads equilibrium from static to dynamic collapse, thus surpassing the explanatory boundaries of classical game theory. The book has a rigorous structure and in-depth arguments, combining theoretical originality with interdisciplinary perspectives, providing a groundbreaking work for researchers, graduate students, and cutting-edge explorers to understand the quantum game revolution.
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. The extremal principles (e.g., the Fermat's principle of least time and the least action principle), which remain central in modern physics, are formulated in terms of one physical value. Using our inequalities, we give a game theoretic interpretation of the interaction of three physical values, namely, free energy, entropy and mean energy. Such approach is inspired by Neumann--Morgenstern and Nash game theories. According to these game theories, the transition from the deterministic strategy (classical mechanics) to probabilistic strategy (quantum mechanics) increases the winning for all players. In the second part of the paper, we simultaneously derive the quasi-classical limits for four cases, that is, for h→0h{\to}0h→0, T→∞T{\to}\inftyT→∞, ω→0\omega{\to}0ω→0, and N→∞,N{\to}\infty,N→∞, where hhh is the Planck constant, TTT is the absolute temperature, ω\omegaω is the frequency of an oscillator, and NNN is the degree of freedom of a system. We note that only the first case is usually considered in quantum physics. The second case was studied initially by M. Planck and the third case by A.~Einstein.
Quantum mechanics and game theory were developed at almost the same time, during the first half of 20th century.Classical game theory is one of the most developed in mathematics and computer science.It has many applications in economics, biology, and different kinds of social science.In computer science, many cryptographic protocols are also based on the elements of game theory.Quantum computing is a relatively new branch of computer science.It unites different aspects of complexity theory and quantum physics.Our intention is to take it one step further and combine classical game theory with the acquired knowledge of quantum computing; in particular, to study the effects of using quantum information in the well-known problems of game theory.In this thesis, we obtain several bounds on the values of some special classes of nonlocal quantum games, and we present a new scheme for games quantization.
The extremal principles, for instance, the Fermat's principle of least time and the principle of least action remain central in modern physics. The named above extremal principles are formulated in terms of one physical value. In the present paper, we give the game theoretic interpretation of the interaction of the three physical values: mean energy E, entropy S and free energy F. Such approach is inspired by the Neumann--Morgenstern game theory and the Nash game theory. According to these game theories, the transition from the deterministic strategy to probabilistic strategy increases the winning for all players. From this point of view we consider the connection between classical mechanics (deterministic strategy) and quantum mechanics (probabilistic strategy). In the present paper, we improve, develop and generalize our previous results.