Jiangfeng Du, Xiaodong Xu, Hui Li, Xianyi Zhou, Rongdian Han
Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum games in different conditions, i.e. different number of the players, different strategic space of the players and different amount of the entanglement involved.
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Risk-Dominant Equilibrium in Quantum Prisoner's Dilemma
针对中等纠缠度下量子囚徒困境存在多个纳什均衡的问题，采用风险占优准则选择唯一均衡，发现纠缠度完全控制风险占优均衡并能促进量子合作、改善博弈结果。
In the quantum version of prisoners' dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducing a third qubit that the interrogator can entangle with the other two. We discuss an enhanced interrogation technique based on tripartite entanglement and analyze Nash equilibria. We show that for tripartite entanglement approaching a W-state, there exist Nash equilibria that coincide with the Pareto optimal choice where both prisoners cooperate. Upon continuous variation between a W-state and a pure bipartite entang…
Using the representation introduced in our another paper\cite{frame}, the well-known Quantum Prisoner's Dilemma proposed in \cite{jens}, is reexpressed and calculated. By this example and the works in \cite{frame} on classical games and Quantum Penny Flip game, which first proposed in \cite{meyer}, we show that our new representation can be a general framework for games originally in different forms.
The well known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.
Quantum game theory is a rapidly evolving subject that extends beyond physics. In this research work, a schematic picture of quantum game theory has been provided with the help of the famous game Prisoners' Dilemma. It has been considered that the shared qubits of the prisoners may interact with the environment which is a bath of simple harmonic oscillators. This interaction introduces decoherence and this model has been compared with phase damping. Calculation of the decoherence factor shows that decoherence reduces the payoff of the prisoners. The factor has been calculated based on whether …
We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $γ$. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it bifurcates into two new Nash equilibria $Q\otimes D$ and $D\otimes Q$. Furthermore for maximum value of decoherence \ $C\otimes D$ and $D\otimes C$ also become Nash equilibria. At this stage the game has four Nash equilibria. On the other hand for three parameters set of strategies there is no pure strategy Nash equilibrium however there is mixed strategy (non unique…
We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game. By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared amo…
We study the three-player Prisoner's Dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off over the classical players. It is also seen that the game's Nash equilibrium does not change in the presence of correlated noise in contradiction to the effect of decoherence in multiplayer case. Furthermore, it is shown that for maximum correlation the game does not behave as a noiseless game and the quantum player is still better off for all values of the decoherence parameter p which is not possible in the two-player case. In additio…
The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in this paper: 1) The well-known Prisoners' Dilemma can be categorized into three types and only the third type is adaptable for quantum strategies. 2) As a reverse problem of game theory, mechanism design provides a better circumstance for quantum strategies than game theory does.
Nash equilibria in four-strategy quantum game extensions of the Prisoner's Dilemma
本文研究四策略量子扩展囚徒困境的纯策略纳什均衡，分析五类同构不变量子博弈的所有均衡，发现量子版均衡更接近帕累托最优，为经典决策困境提供新见解。
We study the possible advantages of adopting of quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner's Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum …
We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular, successful quantum strategies in dilemma games are interpreted in terms of a symmetrized game matrix that corresponds to an altruistic game plan.
High-frequency trading (HFT) offers an excellent user case and a potential killer application of the commercially available, first generation quasi-quantum communication and computation technologies. To this end, we offer here a simple but complete game-theoretic model of HFT as the famous two player game, Prisoner's Dilemma. We explore the implementation of HFT as a game on the (quasi) quantum cloud using the Eisert, Wilkens, and Lewenstein quantum mediated communication protocol, and how this implementation can increase transaction speed and improve the lot of the players in HFT. Using coope…
Agent-based Modelling of Quantum Prisoner's Dilemma
针对无限多玩家进行量子博弈的问题，本研究通过数值化基于智能体模型（ABM）与解析纳什均衡映射（NEM）技术的比较，结合五个合作指标分析单次量子囚徒困境（QuPD）中合作的涌现，揭示了纠缠相关的一阶相变及两种相的性质。
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