1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Game Theory -Deletion of strictly dominated strategies

  1. Apr 26, 2010 #1


    User Avatar

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

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


    2. Relevant equations


    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


    User Avatar

    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook