Game Theory -Deletion of strictly dominated strategies

[jb7]

Homework Statement

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

Homework Equations

n/a

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 :)

 

[jb7]

no ideas?

 

[hgfalling]

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).