MEFPIA算法求解量子博弈均衡：迭代次数更少，误差低于MMWU
Guiding Agents of Quantum Games to Equilibrium using Matrix Exponential Fixed-Point Iteration
有人把量子策略写进博弈论均衡求解，新算法 MEFPIA 比 MMWU 迭代更少、误差更低，搞优化的可以看
论文针对扩展版 Gutoski-Watrous（EGW）量子博弈，将每个玩家的量子策略表示为局部密度矩阵。作者推导了收益函数及其梯度的张量收缩表达式，避免显式构建联合希尔伯特空间中的全密度矩阵并做高维乘法。在此基础上提出带退火的矩阵指数不动点迭代算法 MEFPIA，用于搜索 EGW 博弈的均衡点。在测试实例上与矩阵乘性权重更新算法 MMWU 对比，两者收敛到相同的策略组合和收益，但 MEFPIA 用更少迭代次数达到了更低的相对误差。
Guiding Agents of Quantum Games to Equilibrium using Matrix Exponential Fixed-Point Iteration
In recent years, quantum game theory has gained significant attention as a framework for studying decision-making in multi-agent systems using quantum principles. However, computing equilibrium strategies is challenging because the dimension of the joint Hilbert space grows as the product of the players' local dimensions. In this paper, we consider an extended Gutoski-Watrous (EGW) game in which each player's quantum strategy is represented by a local density matrix. We derive tensor-contraction expressions for the payoff functions and their gradients, thereby avoiding the explicit construction of the full joint density matrix and its computationally expensive multiplication by the payoff operators. Building on the resulting effective Hamiltonians, we propose the Matrix Exponential Fixed-Point Iteration with Annealing (MEFPIA) algorithm to search for equilibrium points in EGW games. We compare MEFPIA with the Matrix Multiplicative Weights Update (MMWU) algorithm in terms of convergence. For the tested instances and parameter settings, both algorithms approach the same strategy profiles and payoffs, while MEFPIA achieves lower relative error in fewer iterations. These results indicate that MEFPIA is a promising numerical method for equilibrium search in multi-agent quantum games. Our findings provide important insights into the quantum game theory's potential for addressing complex decision-making processes, as well as opening up new paths for future research and exploration in multi-agent quantum systems.