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A signaling game is within the field of game theory, and more information can be found here.

I would like to know, how one can solve such a game, by finding the Baysian Nash equilibrium in Mathematica. I have been searching for such a solution including in the wolfram library, but without any luck.

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What do you mean by "solve"? The article you link to describes the game but not a solution. Can you point to the kind of solution you wish for in some other computer language? – bill s Jun 8 '14 at 13:49
from memory this book had code for solving Nash equilibrium: – Mike Honeychurch Jun 8 '14 at 21:47

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