This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable complexity. In doing so, it forges an itinerant loop from game theory to machine learning and back. We show a Nash equilibrium can be approximated with purely calls to stochastic, iterative variants of singular value decomposition and power iteration, with implications for biological plausibility. We provide pseudocode and experiments demonstrating solving for all equilibria of a general-sum game using only these readily available linear algebra tools.

翻译：本文提出了一套新颖的技术，用于逼近有限正规形式博弈中的纳什均衡。其核心在于构建一种新的重构方法，将问题转化为求解一个复杂度可调的多变量多项式参数化系统。通过这一途径，本研究在博弈论与机器学习之间建立了一个循环往复的联结路径。我们证明，仅需调用随机化、迭代化的奇异值分解及幂迭代变体，即可实现对纳什均衡的逼近，这一发现对生物合理性研究具有启示意义。我们提供了伪代码及实验验证，表明仅使用这些现成的线性代数工具即可求解一般和博弈的所有均衡。