Quantum game theory is the study of strategic behavior by agents with access to quantum technology. Broadly speaking, this technology can be employed in either of two ways: As part of a randomization device or as part of a communications protocol. We survey some of the main ideas from both branches of the subject.
Quantum game theory (QGT) extends traditional game theory by using quantum mechanics to create new models for strategic decision-making. Traditional game theory provides effective tools for analyzing rational human interaction; yet it suffers from three main restrictions because it cannot properly handle uncertain situations, contradictory behavior, and complex relationships among agents. QGT addresses these challenges through its implementation of quantum phenomena, which enable strategic options that go beyond traditional mixed strategies. The extended system introduces fresh equilibrium solutions that allow easier resolution of standard problems. The chapter presents an organized structure to display QGT, which shows its value for strategic decision-making systems. The chapter shows fundamental concepts that link classical theories with quantum theories through its demonstration of how quantum strategies have developed from their original state to their present form, which expands traditional game models. The research investigates optimization methods, cybersecurity measures, economic systems, and artificial intelligence applications. The study identifies implementation obstacles and future research needs. The advanced QGT decision-making systems provide outstanding solutions that allow intelligent systems to interact with their environments and solve complex environmental problems.
In this research article, we survey existing quantum physics-related games and, based on this survey, propose a definition for the concept of quantum games. We define a quantum game as any type of rule-based game that either employs the principles of quantum physics or references quantum phenomena or the theory of quantum physics through any of three proposed dimensions: the perceivable dimension of quantum physics, the dimension of quantum technologies, and the dimension of scientific purposes, such as citizen science or education. We also discuss the concept of quantum computer games, which are games on quantum computers, as well as definitions for the concept of science games. Various games explore quantum physics and quantum computing through digital, analogue, and hybrid means, with various incentives driving their development. As interest in games as educational tools for supporting quantum literacy grows, understanding the diverse landscape of quantum games becomes increasingly important. We propose that the three dimensions of quantum games identified in this article be used for designing, analysing, and defining the phenomenon of quantum games.
Quantum games extend classical game theory into the quantum realm by incorporating quantum players and quantum strategies. Two-player quantum games have been widely studied and applied, among other areas, in optimization and decision-making. In this work, we introduce, formalize and analyze a novel class of three-player quantum games, referred to as Proxy Quantum Games (PQGs). In this setting, one player, the Controller, influences or governs the strategic operations executed by a second player, the Proxy, who, in turn, competes directly against a third player, the Opponent. The strategic influence is implemented via controlled unitary operations, whereby the Proxy’s available strategies are conditioned on the Controller’s quantum state. We further generalize the PQG framework by incorporating multiple Controllers acting on a common Proxy, thereby enabling the study of higher-order strategic interactions and multi-agent influence structures. The objective under consideration is the maximization of the Controller’s expected payoff, under various configurations of strategic control and entanglement. Comparative analyses are conducted between the PQG formulation and conventional multiplayer quantum games, highlighting key differences in strategic behavior and payoff distributions.
Humans do not always make the most rational decisions. As studies have shown, even when logic and reasoning point in one direction, sometimes humans “walk” to the opposite route, motivated by personal bias or simply wishful thinking. This paradoxical human behavior has resisted explanation by classical decision theory for over a decade. Scientists have shown that a quantum probability model can provide a simple explanation for human decision-making. In military, decision-making process is considered to be the most neuralgic one. With the recent interest in quantum computing and quantum information theory, there has been an effort to recast classical game theory using quantum probability amplitudes, and hence study the effect of quantum superposition, interference and entanglement on the agents’ optimal strategies. Apart from unsolved problems in quantum information theory, quantum game theory and decision –making, may be useful in studying quantum communication since that can be considered as a game where the objective is to maximize effective communication. This paper discusses the idea of using quantum theory to decision making. 1 HellemicArmy 14, Kanigos Str., Piraeus 18534, Greece.
A quantum game-theoretic setting enables the analysis of strategic interaction among agents with access to quantum resources. One of the original motivations for re-expressing quantum algorithms, and quantum communication protocols, in terms of competing quantum agents was to provide new insights into their workings. Looking closely, one finds that quantum strategic interactions utilize quantum probabilities and such probabilities are realizable in quantum mechanical experiments that allow implementation of unitary transformations, quantum measurements etc. This paper presents a perspective on a quantum game-theoretic framework involving quantum probabilities, which are not subject to the strong factorizability constraints that classical probabilities are found to possess. We suggest that a quantum version of a classical game can be obtained more directly if we replace the factorizability relations for probabilities in a classical game with two weaker constraints that are also obeyed by the quantum probabilities. The solutions of symmetric bimatrix games with such `non-factorizable' probabilities are then analyzed and compared to the solutions that appear in the standard version of a quantum game.