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Suppose you are given a payoff matrix dimensions m*n in which player A has m strategies and player B has n strategies and in each cases it results in a different outcome, so how could you find the probabilities of each state and find which state will reach Nash equilibrium having highest probability of occurring and

assuming that I know the concept and know to solve a 2 by 2 Nash equilibrium matrix and could anyone devised a algorithm or a method so I could implement it in code and programmed in my console.

In some reference i searched you can find system of linear equation and by gaussian elimination you can solve them, so how could you find the system of linear equation in which the unknowns are probability of each state.

Bernard
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Piyush choudhury
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    Does the meaning of the unknowns make the system of linear equations different? I don't think so. Have you tried to search for "system of linear equations algorithm" (https://math.stackexchange.com/questions/30330/fast-algorithm-for-solving-system-of-linear-equations) or "algorithm + Nash + equilibrium" (https://www.wikiwand.com/en/Lemke%E2%80%93Howson_algorithm#:~:text=The%20Lemke%E2%80%93Howson%20algorithm%20is,for%20finding%20a%20Nash%20equilibrium%22.)? –  Feb 27 '21 at 23:07
  • who is this who unmarked for no reason,whoever it is doesn't know it discourages the authors ,leaners and dought seeker and bernard ,he have not edited anything but still attached it's name to get medal and now you will close this question and ban my account but instead they could just answer my question. – Piyush choudhury Feb 28 '21 at 04:19
  • this toby mark s dismarking my every question without no reason.he has already ban my previous account where there were qood questions. – Piyush choudhury Feb 28 '21 at 04:22
  • @Piyushchoudhury As fas as I can see, Bernard corrected a typo in the title with the edit (which was originally "equibrilliam"). – SampleTime Feb 28 '21 at 09:14

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