A quantum extension to inspection game

Purpose This study explores innovative strategies for the adoption of electric construction machinery in plateau traffic tunnel engineering, utilizing quantum game theory to analyze stakeholder interactions and decision-making processes. Design/methodology/approach A quantum game model was constructed to examine the strategic behaviors of three key stakeholders: government departments, machinery manufacturers and construction enterprises. This model incorporates quantum principles (e.g. superposition and entanglement) to capture the dynamic, interdependent nature of decision-making in this context. Numerical analysis was performed to evaluate how quantum strategies affect stakeholder payoffs and cooperation. Findings The results demonstrate that quantum game theory enhances cooperation among stakeholders, leading to more optimal outcomes than classical game theory. When quantum entanglement is considered, stakeholders are more likely to adopt active strategies, achieving Pareto optimality. The study identifies specific conditions under which quantum strategies maximize benefits for all parties, promoting the widespread adoption of electric construction machinery in plateau environments. Originality/value This research is the first to apply quantum game theory to the innovation of electric construction machinery in plateau traffic tunnel engineering. It provides a novel framework for analyzing stakeholder interactions and offers innovative strategies to overcome technical and economic barriers, contributing to sustainable development in the construction industry.

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however less is known for infinitely repeated quantum games. Investigating infinitely repeated games is crucial since finitely repeated games do not much differ from single round games. In this work we establish the concept of general repeated quantum games and show the Quantum Folk Theorem, which claims that by iterating a game one can find an equilibrium strategy of the game and receive reward that is not obtained by a Nash equilibrium of the corresponding single round quantum game. A significant difference between repeated quantum prisoner's dilemma and repeated classical prisoner's dilemma is that the classical Pareto optimal solution is not always an equilibrium of the repeated quantum game when entanglement is sufficiently strong. When entanglement is sufficiently strong and reward is small, mutual cooperation cannot be an equilibrium of the repeated quantum game. In addition we present several concrete equilibrium strategies of the repeated quantum prisoner's dilemma.

In the 21st century, various socio-economic crises have revealed that traditional economic science and (neo)classical thinking are unable to explain all the complexity of current economic problems, therefore the application of more complex and non-trivial economic concepts is gaining relevance. In addition to behavioral and evolutionary economic thinking, models of quantum economics have been developed in recent years, which allow solving economic problems, using mainly quantum thinking and the principles of quantum physics, in particular particle-wave dualism, the principle of uncertainty, the absence of a subject-object distinction, superposition and confusion. The article addresses 3 research questions (RQ). According to RQ1, the paper finds that quantum economics research is dominated by the following topics: quantum economics, quantum finance, quantum decision making, and quantum game theory. According to these four thematic descriptors, the article carries out a systematic modern review of scientific works in the period from 1978 to 2022 (if only 50 works were published in 1978-1999, then in 2000-2022 already 3430), with an emphasis on the most cited (Google Scholar) English-language journal articles. The analysis showed that articles on this topic are published mainly in journals of a non-economic profile, that the peaks of publication activity occur at times of powerful socio-economic upheavals (for example, the dot.com bubble, the substandard/financial crisis, the European debt crisis, the coronavirus pandemic, etc.). In accordance with RQ2, the article defines the key characteristics of the quantum economic model: in contrast to neoclassical economics (based on mechanistic classical physics, is rational and deterministic, with the help of the invisible hand of the market it leads to a stable equilibrium), the quantum approach, on the contrary, considers the economy as more complex, empirically oriented, uncertain, probabilistic, superpositional, as an archetypal example of a quantum social system that has its own versions of duality, measurement, and entanglement. According to RQ 3, the article determines to what extent quantum economics can update (neo)classical economics (integration of new ontological premises into economic thinking, more experimental and practical approach, connection between the concept of entanglement and sustainable development, management of financial risks based on the concept of quantum probability, rethinking the concept of randomness by quantum probability, introduction of quantum money, equilibrium using quantum games, etc.).

Homologies between decision sciences, economics, and physics have been observed and applied for quite some time. Even von Neumann, who established the foundations of mathematics for quantum mechanics and game theory, noted what he considered obvious relationships between these fields of study. However, it is the physical world that is often used as a source of models for application in behavioral, micro, and macroeconomics rather than the other way around. This research seeks to advance prior work that identified an analogy between the Entropy Decision Risk Model's (EDRM) definition of proximity, which relates objective and subjective probability to explain how subjects perceive uncertainty, and the Born Rule of Quantum Mechanics. So far, there has been no derivation for the Born Rule, as it is based only upon an editor's remark in a footnote of Born's foundational 1926 paper, leaving an unanswered question. The goal of this research is to understand homologies and isomorphologies between quantum mechanics and decision engineering that will benefit both disciplines.

Traffic Grooming in optical networks is one if the most important and hot problems in the area of optical network. In the static traffic grooming problem, we introduce the concept of QoS (Quality of Service); in order to minimize the network cost utilization rate and to maximize the QoS degree of the users at the same time, we apply the intelligent computing algorithm -QIA( the quantum-based Immune Algorithm) to the framework to solve the problem.

A truel, or a three person generaliztion of a duel, is a popular model in game theory of a struggle of survival. The outcome is often sensitive to the precise rules under which the truel is performed and can be anti-intuitive. We propose a quantum scheme, along the lines of recent work in quantum game theory, for the problem of duels and truels. Interference amongst the players' strategies can arise leading to game equilibria different from the classical case.

Inspection games in arms control

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

We present a novel method of looking at Nash equilibria in 2 × 2 quantum games. Our method is based on a mathematical connection between the problem of identifying Nash equilibria in game theory, and the topological problem of the periodic points in nonlinear maps. To adapt our method to the original protocol designed by Eisert et al (1999 Phys. Rev. Lett. 83 3077–80) to study quantum games, we are forced to extend the space of strategies from the initial proposal. We apply our method to the extended strategy space version of the quantum Prisoner's dilemma and find that a new set of Nash equilibria emerge in a natural way. Nash equilibria in this set are optimal as Eisert's solution of the quantum Prisoner's dilemma and include this solution as a limit case.

This article presents a unified probabilistic framework that allows both rational and irrational decision-making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of game-theoretic models, which assumes that a decision-maker chooses the best action according to their preferences. In this article, we define irrationality as a deviation from a rational choice. Bistable probabilities are proposed as a principled and straightforward means for modelling (ir)rational decision-making in games. Bistable variants of classical and quantum Prisoner's Dilemma, Stag Hunt and Chicken are analysed in order to assess the effect of (ir)rationality on agent utility and Nash equilibria. It was found that up to three Nash equilibria exist for all three classical bistable games and maximal utility was attained when agents were rational. Up to three Nash equilibria exist for all three quantum bistable games; however, utility was shown to increase according to higher levels of agent irrationality.

Several different definitions of quantum games have been proposed over the past five years. Some of the results claimed for the differences between these quantum games and classical games identified as those to which they correspond have been criticized, however, as not being fair comparisons. In this paper I define classical and quantum versions of games with mediated communication, and propose that these are the classical and quantum games that should be compared.

Quantum game simulator, using the circuit model of quantum computation

Game theory has been used for simulating finance problems for a long time. Not only game can simulate the decision-making process based on strategy and rules, the construction of a game gives various solutions for real financial problems. The thesis introduces basic game theory analysis and discovers numbers game as a tool to construct pricing model. Further works are concentrating on quantum game in order to give extended discussions on quantum Flipping Game.

The well-known quantization schemes for two-player nonzero-sum games are Eisert–Wilkens–Lewenstein scheme and Marinatto–Weber scheme. In this work, we establish the connection between the two schemes from the perspective of quantum circuits. Further, we provide the correspondence between any game quantization schemes and the CNOT complexity, where CNOT complexity is up to the local unitary operations. While CNOT complexity is known to be useful in the analysis of universal quantum circuit, in this work, we find its applicability in quantum game theory.

Recently, some schemes on how to realize quantum NOT gate have been reported. In this paper, we theoretically propose a new scheme by means of quantum theory. Here we use a quantum coin as a quantum NOT gate and its logic function is realized by the quantum game theory. In our schemes, classical noise does not disturb the realization of quantum NOT gate.