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Homework Help: Game Theory -Deletion of strictly dominated strategies

  1. Apr 26, 2010 #1

    jb7

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    1. The problem statement, all variables and given/known data

    Hi, I was wondering if I could get some help with these questions.

    fazz4l.jpg


    2. Relevant equations

    n/a

    3. The attempt at a solution

    a) I (think) I can do this one, mutual best responses would suggest that the nash equilbria are (a,a), (a,b) and (b,c)

    b) Now this is the question where I get stuck. Player 1's strategy c can be eliminated, as it is strictly dominated by a (and b). But I am not sure what to do from here, I am guessing that I have to eliminate a strategy for player 2, but I can't see any that are strictly dominated. There don't even seem to be any strategies that are eliminated by mixed strategies..

    please help! thanks :)
     
  2. jcsd
  3. Apr 30, 2010 #2

    jb7

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    no ideas?
     
  4. Apr 30, 2010 #3
    Usually you ignore dominated strategies when finding a pure-strategy equilibrium. So player 2 plays a) which dominates his other strategies. And player 1 plays a), so the pure-strategy equilibrium is (a,a).

    In b), the only eliminated strategy is p1_c, like you said. So that's it.

    For c), suppose that P1 played both a and b with non-zero weight. What would P2's best response be? Suppose both sides played the resultant strategies. ie, P1 played a/b in some proportion, and P2 played his best response. Would this be a Nash equilibrium?

    Now use the answers from b) and c) to find part d).
     
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