I am facing difficulty in understanding the bolded portion of the following statement from this paper
GANs are defined by a min-max two-player game between a discriminative network $D_\Psi(x)$ and generative network $G_\theta(z)$. While the discriminator tries to distinguish between real data point and data points produced by the generator, the generator tries to fool the discriminator. It can be shown that if both the generator and discriminator are powerful enough to approximate any real-valued function, the unique Nash-equilibrium of this two-player game is given by a generator that produces the true data distribution and a discriminator which is 0 everywhere on the data distribution.
My understanding is that discriminator gives $1/2$ for any further inputs after training. But, what is the 0 mentioned?