over D in the inner loop if we do this min max problem applied to the value function V we are guaranteed to actually recover the training distribution but if we swap the order of the mechs and the men we get a different result in fact if we minimize every G in the inner loop the generator has no incentive to do anything other than map all inputs Z to the same output X and that output X is the point that is currently considered most likely to be real rather than fake by the current value of the generator so we really want to do min max and not max