This paper introduces economists to quantum-inspired approaches for modeling firm behavior in a Cournot Duopoly, designed for accessibility and pedagogical use. We present key quantum concepts -- superposition, entanglement, and quantum search algorithms (Grover's and Dürr-Høyer's) -- in an intuitive manner, tailored for those without a quantum physics background. These concepts are applied to represent uncertainty, interdependence, and optimization in novel ways, offering fresh perspectives on firm decision-making. By incorporating numerical examples, we illustrate how quantum-inspired models differ from classical Cournot outcomes, highlighting potential advantages in capturing complex strategic interactions. The paper aims to bridge quantum computing and economic theory, providing a foundation for teaching and exploring advanced modeling techniques.
This paper introduces economists to quantum-inspired approaches for modeling firm behavior in a Cournot Duopoly, designed for accessibility and pedagogical use. We present key quantum concepts -- superposition, entanglement, and quantum search algorithms (Grover's and Dürr-Høyer's) -- in an intuitive manner, tailored for those without a quantum physics background. These concepts are applied to represent uncertainty, interdependence, and optimization in novel ways, offering fresh perspectives on firm decision-making. By incorporating numerical examples, we illustrate how quantum-inspired models differ from classical Cournot outcomes, highlighting potential advantages in capturing complex strategic interactions. The paper aims to bridge quantum computing and economic theory, providing a foundation for teaching and exploring advanced modeling techniques.
This article explores the interdisciplinary interface between quantum computing and economic theory, with a particular emphasis on how foundational concepts from quantum mechanics reshape core methodological and epistemological assumptions in economics. Drawing on a comprehensive bibliographic methodology, the study synthesizes contributions from quantum physics, computational theory, and economic modeling to trace the impact of quantum logic -especially principles such as superposition, entanglement, and measurement irreversibility- on both theoretical constructs and applied frameworks. Particular attention is given to emblematic algorithms (e.g., Shor’s and Grover’s) as case studies for illustrating computational discontinuities in fields such as cryptographic trust, portfolio optimization, and decision-making under uncertainty. The article also surveys recent developments in quantum machine learning and quantum-inspired models relevant to economic forecasting and adaptive policy design. Ethical and distributional concerns are critically addressed, especially in relation to the asymmetric global access to quantum resources. By mapping this emerging field through a structured review of cross-disciplinary literature, the paper offers a conceptual framework for understanding how quantum technologies may influence future research in financial economics, risk theory, and the modeling of complex systems operating under deep informational constraints.
The development of quantum information theory based on quantum entangled states is advancing rapidly and has promoted the emergence of quantum game theory. Quantum game theory is quantum information processing applied to classical games, which solves problems that classical games cannot solve. This paper explores the quantum Cournot-Bertrand game model of two firms in a duopoly market with bounded rationality and product substitutability. The first and second firms choose production output and sales price as their decision variables, respectively. We first define the quantum Cournot-Bertrand dynamical system and study the existence and locally stable conditions of equilibrium points. Then we explore bifurcation conditions and bifurcation types. Finally, we do the bifurcation analysis and explore the impacts of the model parameters as the potential market size of products, the two firms' linear marginal cost, the players' speed of strategy adjustment, the product substitution index, and the quantum entanglement degree on the Nash equilibrium stability and bifurcation using numerical analysis and simulation, and provide economic explanations for the results.
The increasing complexity of modern decision-making environments has challenged the effectiveness of classical mathematical models. Traditional probabilistic frameworks often struggle to represent uncertainty, ambiguity, contextual dependence, and nonlinear interactions among decision variables. Quantum-inspired mathematical models have emerged as a promising interdisciplinary approach that leverages mathematical principles derived from quantum theory without requiring quantum computing hardware. These models utilize concepts such as superposition, interference, entanglement, and contextuality to represent complex decision processes more accurately. This paper explores the theoretical foundations, mathematical structures, and applications of quantum-inspired decision models in complex systems. The study examines how quantum probability theory provides a more flexible representation of human cognition, organizational decision-making, financial forecasting, and artificial intelligence systems. Furthermore, the paper discusses mathematical formulations, implementation strategies, advantages, challenges, and future research directions. The findings suggest that quantum-inspired models offer significant potential for addressing uncertainty and dynamic interactions in complex decision environments, thereby contributing to the advancement of intelligent decision support systems.
This paper explores the development and application of novel optimization algorithms inspired by the principles of quantum mechanics. Recognizing the potential of quantum phenomena like superposition and tunneling for enhancing computational efficiency, we propose a new algorithmic framework that mimics these behaviors within a classical computing environment. The core idea is to construct an optimization algorithm that incorporates probabilistic search strategies, analogous to quantum tunneling, and explores multiple solution possibilities concurrently, similar to superposition. This approach aims to overcome the limitations of traditional optimization methods, particularly in tackling complex, high-dimensional problems. We detail the algorithm's design, emphasizing the key mathematical formulations and probabilistic elements. The proposed algorithm's performance is evaluated through theoretical analysis and conceptual demonstrations, showcasing its potential to offer improved convergence rates and solution quality compared to established classical optimization techniques. The research contributes to the burgeoning field of quantum-inspired computing, providing a practical and accessible approach for leveraging quantum concepts for optimization challenges.
Quantum-inspired algorithms are emerging as a promising alternative to classical optimization techniques, particularly for complex problem domains. This paper introduces a novel quantum-inspired algorithm designed to leverage the principles of superposition and entanglement to enhance search and solution efficiency. We explore the potential of these concepts to represent and manipulate problem states, offering a fundamentally different approach to optimization. The algorithm's core mechanism centers around creating a quantum-like state space, enabling efficient exploration of the solution space. This work presents a preliminary analysis of the algorithm's potential for exponential speedups, although further investigation and validation are necessary.
This paper explores the potential of quantum-inspired algorithms for tackling large-scale optimization problems. Traditional optimization methods often struggle with the computational complexity of problems involving numerous variables and constraints. Quantum mechanics, particularly concepts like superposition and entanglement, offers a radically different approach to problem-solving. This work investigates how these concepts can be translated into algorithmic designs, aiming to improve the efficiency and speed of optimization processes. We propose a framework for developing algorithms that mimic quantum phenomena, focusing on techniques that enable exploration of the solution space in a more parallel and potentially faster manner. The core of this approach lies in leveraging mathematical structures derived from quantum mechanics to guide search strategies. We outline key algorithmic ideas, emphasizing the potential for improved convergence rates and scalability. The presented concepts represent a novel application of quantum-inspired ideas to the field of optimization, offering a promising avenue for addressing complex real-world problems.