Okay, I have a pretty solid math background but it’s been a long time (I’ve spent the last three years learning useful stuff like the parol evidence rule and the rule against perpetuities). But I have a general interest in stuff like game theory, so here goes my simple question.
Given a basic payoff matrix, as follows:
with player A deciding which row and B deciding which column to select, what’s the formula for an optimal strategy?
If A chooses row 1 x% of the time, and B chooses column 1 y% of the time, then A’s expected payoff is
P(a)= xyP+x*(1-y)*Q + (1-x)yR + (1-x) * (1-y)*S
Since this is a zero sum game, B’s is simply (-P(a)), and of course both players wish to maximize their profit/ minimize their loss given perfect play from the other.
So the basic question is how do you calculate this? Is there a simple formula, or do you have to do some sort of recursive iteration?