A competitive game whose maximal Nash-equilibrium payoff requires quantum resources for its achievement

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find th…

Quantum two-players games, Entanglement and Nash equilibria

The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple geometric properties of "chiral" group $SU (N)\times SU(N)$ and is based on considering the stability subgroup of the initial state of the game. The explicit forms of neither the gate operator nor the payoff matrix are necessary.

基于一般纠缠算子的量子 Cournot 模型

Quantum Cournot model based on general entanglement operator

研究含对称二次表达式的一般纠缠算子下量子 Cournot 模型，比较单、双压缩参数博弈的纠缠度与 Nash 均衡收益，揭示相位参数对最优收益可达性的关键影响。

Quantum Nash equilibrium in the thermodynamic limit

The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and the quantum game of chicken. A phase transition is seen in both games as a function of the entanglement in the game. We observe that for maximal entanglement irrespective of the classical payoffs, a majority of players choose Quantum strategy over Defect in the thermodynamic limit.

Nash Equilibria in Quantum Games

For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by Eisert and Wilkins [EW]. In the game $\G^Q$, each players' strategy set consists of the set of all probability distributions on the 3-sphere $S^3$. Nash equilibria in this game can be difficult to compute. Our main theorems classify all possible equilibria in $\G^Q$ for a Zariski-dense set of games $\G$ that we call {\it generic games}. First, we show that up t…

Quantum Model of Bertrand Duopoly

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entanglement in the initial state gives payoffs higher to the firms than the classical payoffs at the Nash equilibrium. As a result the dilemma like situation in the classical game is resolved.

Bayesian Nash均衡与贝尔不等式

Bayesian Nash Equilibria and Bell Inequalities

具有不完整信息的游戏以多部门概率矩阵形式来表达，可以处理量子策略和经典策略。通过对经典策略和量子策略的分析，阐明了非局部策略的两种不同作用，并建立了博弈收益的真正量子增益与贝尔不等式破缺之间的直接联系。

双矩阵对策的量子关联与纳什均衡

Quantum correlations and Nash equilibria of a bi-matrix game

玩对称双矩阵游戏通常通过在两个玩家之间共享成对的“对象”来实现。提出了一个新的设置，明确显示对之间的量子相关性的影响的结构上的支付关系和“解决方案”的游戏。该设置允许游戏的重新表达，使得当玩家在具有满足贝尔不等式的相关性的对象对上执行他们的移动时，玩家玩经典游戏。如果参与者收到的配对具有量子相关性，则由此产生的博弈不能被认为是另一个经典的对称双矩阵博弈。此外，纳什均衡的游戏被发现是由性质的相关性。

Quantum Speedups for Zero-Sum Games via Improved Dynamic Gibbs Sampling

We give a quantum algorithm for computing an $ε$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $\widetilde{O}(\sqrt{m + n}\cdot ε^{-2.5} + ε^{-3})$ and outputs a classical representation of the $ε$-approximate Nash equilibrium. This improves upon the best prior quantum runtime of $\widetilde{O}(\sqrt{m + n} \cdot ε^{-3})$ obtained by [vAG19] and the classic $\widetilde{O}((m + n) \cdot ε^{-2})$ runtime due to [GK95] whenever $ε= Ω((m +n)^{-1})$. We …