In order to analyze the power control problem, the wireless quantum network nodes are modeled as players at a quantum game. The power control problem is one of the most significant wireless communications challenges which characteristics make it proper to be modeled by means of game theory techniques. The problem results in non-cooperative game by nature, but, under quantum rules, a larger strategy space leads the players to choose a coalition strategy as the best option. Thus, the use of quantum game strategies makes possible the emergence of new equilibrium, which guarantees the best possible performance to the whole network. We show also that the whole network power consumption decreases when the intrinsic parallel behavior of quantum computation is capitalized. Moreover, the design of efficient medium access control algorithms is possible.
In order to analyze the power control problem, the wireless quantum network nodes are modeled as players at a quantum game. The power control problem is one of the most significant wireless communications challenges which characteristics make it proper to be modeled by means of game theory techniques. The problem results in non-cooperative game by nature, but, under quantum rules, a larger strategy space leads the players to choose a coalition strategy as the best option. Thus, the use of quantum game strategies makes possible the emergence of new equilibrium, which guarantees the best possible performance to the whole network. We show also that the whole network power consumption decreases when the intrinsic parallel behavior of quantum computation is capitalized. Moreover, the design of efficient medium access control algorithms is possible.
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation, and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between quantum computers, it is imperative and crucial to exploit game theory for addressing challenges such as entanglement distribution and access, routing, topology extraction, and inference. Quantum networks provide the promising opportunity of employing quantum games owing to their inherent capability of generating and sharing quantum states. In addition, quantum games offer enhanced payoffs and winning probabilities, new strategies, and equilibria, which are unimaginable in classical games. Employing quantum game theory to solve fundamental challenges in quantum networks opens a new fundamental research direction necessitating inter-disciplinary efforts. In this article, we introduce a novel game-the-oretical framework for exploiting quantum strategies to solve – as an archetypal example – one of the key functionalities of a quantum network, namely, entanglement distribution. We compare quantum strategies with classical ones by showing the quantum advantages in terms of link fidelity improvement and latency decrease in communication. In the future, we will generalize our game framework to optimize entanglement distribution and access over any quantum network topology. We will also explore how quantum games can be leveraged to address other challenges like routing, optimization of quantum operations, and topology design.
Medium access control (MAC) and efficient spectrum allocation function particularly, are real challenges that wireless communications are facing nowadays and Dynamic Spectrum Access (DSA), enhanced with quantum computation techniques, is the most promising alternative. In such a context, we capitalize quantum games and quantum decisions strengths to design protocols that make classic communications more efficient. That is, we focus on protocols running on quantum devices whose input and output signals are classic. In this work we propose a quantum media access control (QMAC) that allows dynamic and fair spectrum allocation. Particularly, we point to two of the main DSA functions, which are Spectrum Sharing and Spectrum Allocation.
This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.
In this paper, we focus on how to solve complex traditional game problems with quantum technology. Quantum game prompts the emergence of cooperation by introducing the quantum strategy to traditional game. We analyze three important factors of the evolutionary quantum game on lattice networks: steps, temptation and entanglement. Results of the experimental applications of analysis procedure are given to illustrate the proposed quantum technique. The system of quantum game will show signs of stability after a series of transient steps. We will reap better benefit by choosing appropriate quantum parameters, because quantum strategys advantage over defeat strategy.
The assignment of resources dynamically is a decisive issue in the new paradigms of computations including cloud, edge, fog computing, and the Internet of Things (IoT). These are heterogeneous resource environments, decentralized control environments, and overload environments that vary at a rapid pace and require adaptive and intelligent allocation schemes. The paper suggests a hybrid quantum-game-theoretic model, which combines quantum optimization approaches and multi-agent game theory to solve the problems of multi-agent resource allocation in dynamic systems. Using the quantum concept of superposition and entanglement, the framework can explore the solution spaces in parallel and therefore increase convergence speed and allocation efficiency.A quantum game-theoretic model is developed, which entails price-motivated system to control the strategic interaction of rational agents, in addition to maintaining stability, autonomy and equilibrium. The resource allocation problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solved with the Quantum Approximate Optimization Algorithm (QAOA) algorithm. The proposed approach is proved to be useful as simulation results show significant gains to classical baselines in terms of utility gain, fairness, and system throughput. The results highlight the possibilities of the quantum-game-theoretic paradigm as a fundamental engine of next-generation computing infrastructures, including networked cloud, edge and IoT with networked computing nodes in VPN-enabled networks.
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of "quantized games", and of applying game theory to quantum mechanics, referred to henceforth as "gaming the quantum", have become synonymous under the single ill-defined term "quantum game". Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multi-player, non-cooperative game quantum mechanical, is given. Within the context of this description, finding a Nash equilibrium in a strictly competitive quantum game is shown to be equivalent to finding a solution to a simultaneous best approximation problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.