Could please explain how the probabilities are calculated. How are all mixed strategy equilibriums are calculated.

2. (a) (10%) The utility of player A is: UA (aA, k) = 8 - as if aAtk 3, -QA if aA t k 3 -k, and UA (QA, k) = -aA 0 for all k = 0, 1, 2, 3, the interim utilities in the mixed-strategy Nash equilibrium (at, a; ) must be the same: UA (0, a) = UA (1, Q) = UB (2, Q) = UA (3, a) , where UA (0, a) = Pr {aB = 3} *8 + Pr {aB