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Matrix Game Calculator

Free online matrix game calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.

中文版:矩阵博弈计算器

Matrix Game Calculator
行玩家收益矩阵(3×3 或 2×3/3×2,行=你的策略,列=对方策略)

原理:若某行每个元素都不大于另一行(对行玩家劣),理性玩家永远不会用它,可以整行删去;列同理(列玩家要最小)。反复删除被支配策略能把大矩阵博弈收缩到 2×2 甚至鞍点,而不改变博弈值——这是求解矩阵博弈的标准前处理。

步骤:① 输入收益矩阵;② 点击化简;③ 查看删除顺序与化简后的博弈值。

示例:A = [[3, 5, 2], [1, 4, 6], [2, 3, 1]] 先删去行3(被行1 支配),再删去列2(被列1 支配),化简为 [[3, 2], [1, 6]],混合均衡博弈值 v = 2.666666666667,原 3×3 博弈的值就是这个数。

注意事项:这里用的是弱支配(允许相等),删弱支配策略在极少数博弈里可能丢掉部分均衡,但博弈值不变;删除顺序不唯一时结果仍一致;若化简后仍大于 2×2,本工具会提示无法继续,需要图解法或线性规划。

相关:零和博弈计算器直接求解 2×2 混合均衡;纳什均衡计算器处理非零和情形;矩阵范数计算器可用于检验收益矩阵的量级差异。

How to use the Matrix Game Calculator

  1. Fill in the inputs with your own numbers — every field shows what it expects.
  2. The result updates instantly as you type; no "Calculate" click needed.
  3. Read the result card for the main figure, the step-by-step formula, and practical notes.

Frequently asked questions

Is the Matrix Game Calculator free?

Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.

Is there a Chinese version of this tool?

Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.

References

Formulas and benchmarks used by this calculator follow these published sources.

  1. dlmf.nist.gov
  2. mathworld.wolfram.com
Kevin's profile

KevinContent LeadCalcton Editorial Team · Last updated 2026-10-05

Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.

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