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Math Help - Game Theory 3x3

  1. #1
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    Game Theory 3x3

    Hi, I'd like to solve the following problem, a version of Rock-Papers-Scissors:

    Rock beats Scissors 100% of the time
    Scissors beats Paper 100% of the time
    Paper beats Rock 99% of the time

    What is the Nash equilibrium (for choosing what to play)?

    I know that it will be a mixed strategy equilibrium, but I haven't found a place that will help solving 3x3s without simplification / reduction (they always find dominated strategies, for example).

    I'm pretty sure I'm just forgetting something simple...

    Thanks for any help.
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  2. #2
    mfb
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    Re: Game Theory 3x3

    Rock beats paper 1% of the time?

    The nash equilibrium can be written as:
    Play rock with probability r.
    Play scissors with probability s.
    Play paper with probability 1-r-s.

    Against a player with this strategy, it does not matter which strategy you choose. Therefore, playing 100% rock or 100% scissors or 100% paper is equivalent. This gives you 2 simple equations which you can use to solve for r and s.
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