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
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
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- 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.
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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Free online math calculators for algebra, statistics, number theory and everyday arithmetic — from quadratic equations and matrices to percentages, fractions and prime factorization, each with step-by-step formulas.