I was trying to solve the payoff matrix above for the pure strategy and the mixed strategy Nash equilibria. It seems that both players have a weakly dominant strategy, by choosing U, player 1 would be indifferent or better off compared to choosing D, and while choosing R, player 2 would be indifferent or better off compared to choosing L. This brings me to the pure strategy Nash equilibrium UR or RU, with the payoff 1,1.
However, I'm mainly concerned with the result of the mixed strategy Nash equilibrium. When I derived the probabilities of player 1 choosing U (p), and player 2 choosing L (q), I got probabilities p=0 and q=1.
Does this imply that LD is a pure strategy Nash equilibrium or a mixed strategy Nash equilibrium? Also, why would player 1 and player 2 both opt for their weakly dominated strategies instead of their weakly dominant strategies?
Thank you in advance!