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Nash's Theorem proof in 2by2 games

  1. Aug 22, 2012 #1
    According to Nash's Theorem, every game has at least one Nash Equilibrium, whether that be a pure strategy or a mixed strategy Nash equilibrium. However, I have not been able to find a proof for the theorem.

    I am looking for a proof of the theorem in 2by2 games involving simultaneous strategies. Perhaps someone here knows good places where these proofs can be found? I googled but most seem to explain the theorem rather superficially without a rigorous mathematical approach.


  2. jcsd
  3. Aug 22, 2012 #2


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  4. Aug 22, 2012 #3
    Yep! The proofs that show up on google generalize it to 'n' players each having many strategies.

    I was looking for a short proof on the simple case of 2by2 games with only 2 players. It should proof the existence of at least one Nash equilibrium.

  5. Aug 23, 2012 #4


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