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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.

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.

Quantum game theory is a new interdisciplinary field between game theory and physical research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement between players. Our result shows that the quantum inspection game has various Nash equilibrium depending on the initial quantum state of the game. It is also shown that quantization can respectively help each player to increase his own payoff, yet fails to bring Pareto improvement for the collective payoff in the quantum inspection game.

Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on historical and narrative perspectives, are only partially effective. The reason is that they do not address in depth those basic quantum concepts that radically question the fundamentals of classical physics. A research-based educational program has been proposed to two final-year classes of an Italian scientific high school. In order to build the main concepts of quantum mechanics and their formal basic representation via real and simulated experiments, the program uses the light polarization as a context. A quantum game was then integrated in the educational program, to support students’ learning. Their conceptual paths, monitored by means of tutorials and questionnaires, show significant student learning especially on the concept of state and on appropriating the formalism meaning, whereas students more frequently referred to the geometrical vector representation instead of the algebraic-analytic formula. The quantum game has emerged to support intuition and operative experience in distinguishing the foundational concepts of superposition and entanglement.

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Insuperable socio-economic and ecological crises demonstrate the need to challenge economic growth ideology that is often embedded in contemporary tourism science. By borrowing from Buddhist philosophy this essay describes inconsistencies in economic theorizing due to its adoption of the Cartesian ontology implying a mechanistic thinking form. Following philosopher Brodbeck (2014), economic science is neither an empirically exact science nor value-free but represents an implicit ethics. To build on this, the elements of a post-mechanistic economic theory are sketched (Brodbeck, 2001). The applicability of this concept is corroborated by instances of current tourism research. After reinterpreting the homo economicus and the nature of money an agenda for a transformative tourism science building upon post-Cartesian economic thinking and Buddhist philosophy is elaborated.

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.

Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens asset returns to microscopic particle motion, governed by quantum probabilities akin to physical laws. However, such approaches presuppose specific microscopic quantum effects in return changes, a premise criticized for lack of guarantee. This paper diverges by regarding that quantum probability as a mathematical extension of classical probability to complex numbers. It isn’t exclusively tied to microscopic quantum phenomena, bypassing the requirement for quantum effects in returns. By directly linking quantum probability’s mathematical structure to traders’ decisions and market behaviors, it avoids assuming quantum effects for returns and invoking the wave function. The complex phase of quantum probability, capturing transitions between long and short decisions while considering information interaction among traders, offers an inherent advantage over classical probability in characterizing the multimodal distribution of asset returns. Utilizing Fourier decomposition, we derive a Schödinger-like trading equation, where each term explicitly corresponds to implications of market trading. The equation indicates discrete energy levels in financial trading, with returns following a normal distribution at the lowest level. As the market transitions to higher trading levels, a phase shift occurs in the return distribution, leading to multimodality and fat tails. Empirical research on the Chinese stock market supports the existence of energy levels and multimodal distributions derived from this quantum probability asset returns model.

The concept of sustainable development has evolved considerably since first arising during the 1980s. The different currents of social, political, economic and ecological thinking, as described earlier, have been isolated efforts to define the content and scope of the notion of sustainability, each from its distinct perspective. Nevertheless, these efforts have not led to an integrated, holistic conception of sustainability capable of incorporating in one sole vision all of the social relations, the human-nature relation, and all of the axiological and ideological suprastructure that supports such a vision. On certain occasions, as in neoclassical theory, sustainability is simply an appendix to the old conceptual tenets of the predominant economic model, used at the level of discourse but incapable of stimulating a true practice of sustainability.

Significance Travel and tourism supports 22 million jobs in the EU and accounts for almost 10% of GDP. Its importance is greater still for the economies of Southern Europe, already vulnerable and debt-laden. Thus COVID-19 disruption threatens to widen the EU's North-South divide and sow the seeds of a systemic crisis. Impacts Tourism stakeholders and policymakers across the continent will need to orchestrate their efforts to bring trust back to travel. A recovery plan based on supply-side policies as well as easy monetary policy is key to avoiding a European debt and socio-economic crisis. Structural reforms are key for Southern European economies to improve their competitiveness and insulate themselves from future crises.

The problem of value was of interest in ancient thinkers. More scientific approach to the subject occurred only at the moment of creation first theoretical and also practical direction of economic thought called mercantilism. Both in mercantilism and physiocracy a lot of space devoted to reflection around value. Most interesting this economic category showed representatives of classicism, who created different concepts. The main goal of this essays to show understanding of the value in selected streams of economic thinking, including classical economics. First of all paid attention to essence and the genesis. Created many theories of value, this caused different approach to economic process

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.

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.