In the original GAN formulation, the generator $G$ and discriminator $D$ play a minimax game: $\min_G \max_D \mathbb{E}[\log D(x)] + \mathbb{E}[\log(1-D(G(z)))]$. At the Nash equilibrium, what is $D^*(x)$?

Generative Adversarial Networks

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In the original GAN formulation, the generator G and discriminator D play a minimax game: min_{G} max_{D} E [lo g D (x)] + E [lo g (1 - D (G (z)))] . At the Nash equilibrium, what is D^{*} (x) ?