Zero-sum games are a well known class of game theoretic models, which are widely used in several economics and engineering applications. It is known that any two-player finite zero-sum game in mixed-strategies can be solved, i.e., one of its Nash equilibria can be found solving a linear programming problem associated to it. The idea of this work is to propose and solve zero-sum games which involve infinite and infinitesimal payoffs too, that is non-Archimedean payoffs. Since to find a Nash equilibrium a non-Archimedean linear programming problem needs to be solved, we implement and extend a more powerful version of an already existing non-Archimedean Simplex algorithm, namely the Gross-Simplex one. In particular, the new algorithm, called Gross-Matrix-Simplex, is able to handle the constraint matrix $A$ when it is made of non-Archimedean quantities. To test the correctness and the efficiency of the Gross-Matrix-Simplex algorithm, we provide four numerical experiments, which have been run on an Infinity Computer simulator. Furthermore, we stressed the difference between numerical and symbolic calculations, characterizing the solutions that an algorithm is able to output running over a finite-precision machine. In particular, we showed that the numerical solutions are particular approximations of the true Nash equilibrium which satisfy some properties which make them interestingly close to the concept of an non-Archimedean $\epsilon$-Nash equilibrium. Finally, we also discuss several examples based on well known models related to economics, politics and engineering, where a non-Archimedean zero-sum model appears to be a reasonable, powerful and flexible representation.

零和博弈是一类众所周知的博弈论模型，广泛用于几种经济和工程应用中。已知可以解决混合策略中的任何两人有限零和博弈，即可以找到其纳什均衡之一来解决与其相关的线性规划问题。这项工作的想法是提出并解决零和博弈，该博弈也涉及无穷和无穷的收益，即非阿基米德收益。由于要找到Nash均衡，需要解决非Archimedean线性规划问题，因此，我们实现并扩展了一个更强大的版本，该版本已经存在的非Archimedean Simplex算法，即Gross-Simplex算法。特别是，称为Gross-Matrix-Simplex的新算法能够处理约束矩阵$\mathrm{一种}$当它由非阿基米德数量构成时。为了测试Gross-Matrix-Simplex算法的正确性和效率，我们提供了四个数值实验，这些实验已在Infinity计算机模拟器上运行。此外，我们强调了数值计算和符号计算之间的差异，描述了算法能够在有限精度机器上运行的解决方案。特别地，我们证明了数值解是真正的纳什均衡的特殊近似，满足某些性质，这些性质使它们有趣地接近于非阿基米德方程式的概念。$\epsilon$-纳什均衡。最后，我们还讨论了一些基于与经济学，政治和工程学相关的著名模型的示例，其中非阿基米德零和模型似乎是一种合理，强大而灵活的表示形式。