Rapid developments of quantum computers allow us to test the theoretical concepts but are limited by the small number of qubits. We study game theory from the quantum algorithm perspective not only because of their unique properties, but also because of their relatively simple form, which is not constrained by this limited hardware. We discuss the practical results of running quantum games on IBM Q cloud computers and the limitations of their use in business and economics.
Rapid developments of quantum computers allow us to test the theoretical concepts but are limited by the small number of qubits. We study game theory from the quantum algorithm perspective not only because of their unique properties, but also because of their relatively simple form, which is not constrained by this limited hardware. We discuss the practical results of running quantum games on IBM Q cloud computers and the limitations of their use in business and economics.
Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations where either one or more players have quantum computational power or where the implementation of strategies uses some form of quantum information). Such a setting allows for entanglement and superpositions of strategies and evaluation of payoffs using quantum measurement. This approach to game theory, according to some scholars in the field, could help us understand certain physical systems, improve economic markets, and develop quantum algorithms. I have conducted an investigation into quantum game theory. I have constructed simulation tools using Maple that, along with research into related work, have helped gain some insight into this new field. The important solutions in classical game theory are usually Nash equilibria. What do they look like in the quantum realm? In what
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 is widely perceived to be one of the ways forward in the future of computation as the end of Moore’s law is almost here. Instead of using bits in classical computers, quantum computers manipulate qubits which are governed by the phenomena of superposition and entanglement. In this paper, we demonstrate the relevance of quantum computing in game theory and database search applications. Through a simple example of coin tossing, we show how it is possible to organise a game where one player adopting a quantum strategy is guaranteed to win. It is also shown that the other player, using a second coin (qubit), can subvert this action to award the wins to themselves without the first player’s knowledge. In another application, a modified Grover’s database search algorithm is applied to clone an arbitrary quantum state of a qubit to a duplicate qubit. In both cases, the comparison of simulated and actual results emphasises on the hardware limitations of the current error-prone quantum computers. The quantum computer programs are designed using quantum gates and simulated in the Quantum Information Software Kit before testing on the IBM Q 5.1 (ibmqx4) quantum computer.
Quantum mechanics and game theory were developed at almost the same time, during the first half of 20th century.Classical game theory is one of the most developed in mathematics and computer science.It has many applications in economics, biology, and different kinds of social science.In computer science, many cryptographic protocols are also based on the elements of game theory.Quantum computing is a relatively new branch of computer science.It unites different aspects of complexity theory and quantum physics.Our intention is to take it one step further and combine classical game theory with the acquired knowledge of quantum computing; in particular, to study the effects of using quantum information in the well-known problems of game theory.In this thesis, we obtain several bounds on the values of some special classes of nonlocal quantum games, and we present a new scheme for games quantization.
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.
The authors briefly review quantum game theory and its application in economics. This review is addressed at newcomers and some basic ideas of quantum theory are necessary to follow the text—the short introduction in chapter “A Brief Introduction to Quantum Formalism” will be sufficient. Due to the lack of space only the flagship issues will be discussed. Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. We are aware that the implementation of genuine quantum models is not an easy task. Nevertheless, such models are already an interesting although sophisticated theoretical tool. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.