Mixed strategy nash equilibria in from $2\times N$ bimatrix form

Question

I'm looking for a way of finding (manually!) mixed strategy Nash equilibria in a $2\times N$ game. Calling player 1 the player with two strategies and player 2 the one with $N$ strategies, I've constructed player 2's best response function, however this leaves me only half way and I'm unsure on how to continue.

Ideas?

Thanks in advance!

Answer 1

For the zero-sum case you should look at Philip Straffin's book: Game Theory and Strategy, Part I, Chapter 3.