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Quantum Approach to Game Theory and Social Science

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (1 December 2021) | Viewed by 10054

Special Issue Editors

Faculty of Physics, University of Bialystok, ul. Ciołkowskiego 1L, 15-245 Białystok, Poland
Interests: quantum information processing; quantum game theory; econophysics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The idea that quantum physics might play an important role in understanding and explaining various aspects of life has long been promoted by physicists. Let us mention, for example, such publications as Light and Life (N. Bohr) or What Is Life? (E. Schrödinger). Quantum game theory is based in part on these beliefs. In recent years we observe the growing interest in quantum methods in various fields of science. Areas such as quantum information, quantum decision theory, quantum finance, quantum economic and quantum cognition are intensively developed. These and many more features related to quantum game theory and social science can be included in this Entropy Special Issue. We cordially invite you to participate.

Prof. Dr. Jan Sładkowski
Dr. Marcin Makowski
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum game
  • decision making/analysis
  • quantum market game
  • Shannon entropy and Fisher information
  • quantum-like models
  • social science
  • quantum finances

Published Papers (5 papers)

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Research

11 pages, 277 KiB  
Article
Transactional Interpretation and the Generalized Poisson Distribution
Entropy 2022, 24(10), 1416; https://doi.org/10.3390/e24101416 - 04 Oct 2022
Cited by 3 | Viewed by 917
Abstract
The aim of this paper is to study the quantum-like approach to the description of the market in the context of the principle of minimum Fisher information. We wish to investigate the validity of using squeezed coherent states as market strategies. For this [...] Read more.
The aim of this paper is to study the quantum-like approach to the description of the market in the context of the principle of minimum Fisher information. We wish to investigate the validity of using squeezed coherent states as market strategies. For this purpose, we focus on the representation of any squeezed coherent state with respect to the basis of the eigenvectors of the observable of market risk. We derive a formula for the probability of being the squeezed coherent state in one of these states. The distribution that we call generalized Poisson establishes the relation between the squeezed coherent states and their description in the language of risk in quantum terms. We provide a formula specifying the total risk of squeezed coherent strategy. Then, we propose a risk of risk concept that is in fact the second central moment of the generalized Poisson distribution. This is an important numerical characterization of squeezed coherent strategies. We provide its interpretations on the basis of the uncertainty relation for time and energy. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
10 pages, 290 KiB  
Article
Transactional Interpretation for the Principle of Minimum Fisher Information
Entropy 2021, 23(11), 1464; https://doi.org/10.3390/e23111464 - 06 Nov 2021
Cited by 6 | Viewed by 1779
Abstract
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of [...] Read more.
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information. The second, we call it transactional, expresses Fisher information from the perspective of the constant risk of market strategies. The orders of the market strategies derived from these two descriptions are different. From a market standpoint, minimizing Fisher information is equivalent to minimizing risk. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
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22 pages, 2161 KiB  
Article
Joint Green Marketing Decision-Making of Green Supply Chain Considering Power Structure and Corporate Social Responsibility
Entropy 2021, 23(5), 564; https://doi.org/10.3390/e23050564 - 01 May 2021
Cited by 21 | Viewed by 3045
Abstract
In order to explore the impact of a manufacturer’s or retailer’s undertaking corporate social responsibility (CSR) and different power structures on their joint green marketing decisions and profits in the green supply chain, this paper establishes green supply chain optimization models under six [...] Read more.
In order to explore the impact of a manufacturer’s or retailer’s undertaking corporate social responsibility (CSR) and different power structures on their joint green marketing decisions and profits in the green supply chain, this paper establishes green supply chain optimization models under six different decision-making scenarios according to two different CSR bearers and three different power structures. Based on the main assumptions of a linear product demand function and CSR measured by consumer surplus, this paper solves the equilibrium solutions of the manufacturer and the retailer through game theory. The results show that: First, the difference in the degree of CSR undertaken by manufacturers and retailers leads to a difference in the ranking of optimal strategies of both parties under the three power structures. Second, under the same power structure, compared with undertaking CSR by oneself, when the other party undertakes CSR, the level of the product’s green degree, the level of green promotion, the party’s own profit, and the profit of the other party are all higher. Third, regardless of the power structure, manufacturers and retailers undertaking CSR is conducive to improving the level of product greenness, increasing green promotion, lowering the retail price, increasing consumers’ willingness to buy green products, and ultimately helping to increase the profits of manufacturers and retailers. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
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11 pages, 1942 KiB  
Communication
Industry 4.0 Quantum Strategic Organizational Design Configurations. The Case of 3 Qubits: Two Report to One
Entropy 2021, 23(4), 426; https://doi.org/10.3390/e23040426 - 03 Apr 2021
Cited by 2 | Viewed by 1478
Abstract
The goal of this work is to explore how the relationship between two subordinates reporting to a leader influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits [...] Read more.
The goal of this work is to explore how the relationship between two subordinates reporting to a leader influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision networks. In fact, through the quantum simulation of strategic organizational design configurations (QSOD) through five hundred quantum circuit simulations. We conclude that the alignment probability of the leader is never higher than the average alignment value of his subordinates, i.e., the leader never has a better alignment than his subordinates. In other words, the leader cannot present asymptotic stability better than that of his subordinates. The most relevant conclusion of this work is the clear recommendation to the leaders of Industry 4.0 not to add hierarchical levels to their organization if they have not achieved high levels of stability in the lower levels. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
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14 pages, 3405 KiB  
Communication
Industry 4.0 Quantum Strategic Organizational Design Configurations. The Case of 3 Qubits: One Reports to Two
Entropy 2021, 23(3), 374; https://doi.org/10.3390/e23030374 - 20 Mar 2021
Cited by 5 | Viewed by 1986
Abstract
In this work we explore how the relationship between one subordinate reporting to two leaders influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision [...] Read more.
In this work we explore how the relationship between one subordinate reporting to two leaders influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision networks. This is done for two cases: One in which the leaders do not communicate with each other, and one in which they do. Through the quantum simulation of strategic organizational design configurations (QSOD) through 500 quantum circuit simulations, we conclude that in the first case both leaders are not simultaneously in alignment, and in the second case that both reporting nodes need to have an alignment probability higher than 90% to support the leader node. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
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