I think that the two Masters of Logic would choose to cooperate until round 50, at which point I'm not really sure what would happen. My reasoning for this is that both Masters of Logic know that their goal is to maximize points and that by cooperating all 50 rounds they will get 50 points. Therefore, 50 points is what they would consider as their minimum attainable points, and would only be looking to gain from there.
On round 48, if they had cooperated on all previous rounds, they would each have 47 points, defecting when your opponent cooperates would lead to only 49, which is below the potential 50 that could be gained from cooperating every round.
Even on round 49. If one of the Masters decided to defect at this point when the other cooperates, they would then have 50 points, but the other Master would then defect on the last round, resulting in 50 points still being the maximum any one of them could gain.
However on round 50 this reasoning breaks down, as defecting when your opponent cooperates results in 51 points, which is better than cooperating all 50 rounds time. However, both Masters would know this, and so THEN there would be a conflict of what to do.
Like I said before, this problem only arises on the last round, as the goal is to maximize points, which can only be done by cooperating until the final round. To do anything different at a previous round would not be maximizing profits. Even though you could gain more points than your opponent, that was not the stated goal.