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I was waked with finding all the Pure Nash Equilibrium in this game. After using the "circle the best response" method of finding each players rational choices it seems as though there is no Nash Equilibrium. That appear to only be points at which two of the players coincide and no point at which all three do. Is there something I am missing here or is there not actually a Pure Nash Equilibrium?

Visualization of the 3 player strategy game

  • You're right. There's no pure strategy Nash equilibrium. There's still a mixed strategy NE though. – Herr K. Jan 27 '24 at 02:05

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