I have the follow matrix, but whenever I try to calculate the probabilities, they are all.. equal? I can't deduce the formulas any more and I am incredibly confused since I don't think this is how it is done. Can someone point me out what I am doing wrong?
player 2: 3p+1(1-p) = 3p+1(1-p) 3p+1-1p = 3p+1-1p
player 1: 1q+3(1-q) = 1q+3(1-q) 1q+3-3q=1q+3-3q
This game has only a pure strategy Nash equilibrium of $(T, R)$. There is no reason to mix strategies because changing strategies can not improve either players reward. Note that this would technically be considered a trivial mixed strategy where for example player one plays $T$ with probability 1 and plays $B$ with probability 0.