Game-theoretic Analysis to Content-adaptive Reversible Watermarking

While many games were designed for steganography and robust watermarking, few focused on reversible watermarking. We present a two-encoder game related to the rate-distortion optimization of content-adaptive reversible watermarking. In the game, Alice first hides a payload into a cover. Then, Bob hides another payload into the modified cover. The embedding strategy of Alice affects the embedding capacity of Bob. The embedding strategy of Bob may produce data-extraction errors to Alice. Both want to embed as many pure secret bits as possible, subjected to an upper-bounded distortion. We investigate non-cooperative game and cooperative game between Alice and Bob. When they cooperate with each other, one may consider them as a whole, i.e., an encoder uses a cover for data embedding with two times. When they do not cooperate with each other, the game corresponds to a separable system, i.e., both want to independently hide a payload within the cover, but recovering the cover may need cooperation. We find equilibrium strategies for both players under constraints.