Quantum computing offers the possibility of massively parallel computing that scales to large problems in a way not possible for classical computers. It also may make possible rapid and secure forms of communication that are not possible with classical devices. As an offshoot of the quantum computing literature, a small set of papers has started to examine quantum games. The question naturally arises: what if anything does quantum game theory have for economists? This brief note attempt to summarize the sometimes impenetrable notation used in quantum physics. I argue that quantum games fall within the existing framework of correlated equilibrium, cheap-talk equilibrium and mechanism design theory, where the correlation and/or communication devices are limited in a way not terribly relevant to economic theory. The notation is taken from Cleve et al [2004], and interpreted using the Wikipedia. A quantum mechanical system has a state � , which is simply a � -dimensional
Quantum computing offers the possibility of massively parallel computing that scales to large problems in a way not possible for classical computers. It also may make possible rapid and secure forms of communication that are not possible with classical devices. As an offshoot of the quantum computing literature, a small set of papers has started to examine quantum games. The question naturally arises: what if anything does quantum game theory have for economists? This brief note attempt to summarize the sometimes impenetrable notation used in quantum physics. I argue that quantum games fall within the existing framework of correlated equilibrium, cheap-talk equilibrium and mechanism design theory, where the correlation and/or communication devices are limited in a way not terribly relevant to economic theory. The notation is taken from Cleve et al [2004], and interpreted using the Wikipedia. A quantum mechanical system has a state � , which is simply a � -dimensional
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to stress the new features of the games that may be revealed in their quantum versions. We first introduce from scratch the most fundamental facts of finite-dimensional quantum mechanics. In the main sections the foundations of quantum games are built via the basic examples. We omit sometimes the lengthy calculations (referring to the original papers) once the physical part is sorted out and the problem is reformulated as pure game-theoretic problem of calculating the Nash or dominated equilibria. Finally we touch upon general theory of finite quantum static games and provide further links and references.
Quantum computing represents one of the most disruptive technological paradigms of the 21st century, with profound implications for economic modelling, financial optimization, and computational decision-making. Unlike classical computing, quantum systems leverage superposition, entanglement, and interference to solve problems of exponentially higher complexity, a capability with transformative potential for economics and finance. This study examines the intersection of quantum computing and economics, systematically evaluating both the promises and the barriers defining this emerging field. Regarding opportunities, quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Grover's algorithm, demonstrate significant theoretical advantages in portfolio optimization, risk assessment, option pricing, and the resolution of large-scale combinatorial problems that are intractable for classical machines. Quantum machine learning extends these prospects, offering accelerated capabilities for pattern recognition and predictive modelling relevant to financial markets. However, substantial barriers temper these expectations. Current quantum hardware operates in the NISQ (Noisy Intermediate-Scale Quantum) era, where decoherence, gate errors, and a limited number of qubits constrain practical applicability. The gap between theoretical quantum advantage and real-world economic implementation remains significant, compounded by a shortage of specialists, high infrastructure costs, and the absence of standardized programming frameworks tailored to economic applications. Through a bibliometric analysis of existing literature and a critical review of recent experimental results, the study maps the current state of quantum computing adoption in economics, identifies the most active research frontiers—quantum game theory and quantum portfolio optimization—and outlines the conditions under which quantum advantage could become economically relevant. The findings suggest that, although quantum computing will not transform economic practice in the short term, its long-term disruptive potential warrants proactive engagement from economists, financial institutions, and policymakers.
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.
Game theory has been studied extensively in recent centuries as a set of formal mathematical strategies for optimal decision making. This discipline improved its efficiency with the arrival, in the 20th century, of digital computer science. However, the computational limitations related to exponential time type problems in digital processors, triggered the search for more efficient alternatives. One of these choices is quantum computing. Certainly, quantum processors seem to be able to solve some of these complex problems, at least in theory. For this reason, in recent times, many research works have emerged related to the field of quantum game theory. In this paper we review the main studies about the subject, including operational requirements and implementation details. In addition, we describe various quantum games, their design strategy, and the used supporting tools. We also present the still open debate linked to the interpretation of the transformations of classical algorithms in fundamental game theory to their quantum version, with special attention to the Nash equilibrium.