I am struggling to understand the reasoning behind how inequalities are being treated in the method proposed in this resource. Specifically, I am referring to the approach suggested in this problem, where this algorithm is recommended.
My concern is that during the first iteration, both agents, x and z, might be able to independently find a solution that does not violate the inequality, which could result in them overcompensating. Furthermore, in the next iteration, the constraint is disabled due to max(0, g0(x)), so there might not be anything left to solve.
Please note that my knowledge is not at an advanced level. Any insights or clarifications that could help me understand this will be very appreciated.