Imperfectly synchronized watermark communication is almost the most hostile watermark channel. A desynchronization attack can yield a very high probability of bit error rate by simply moving the watermark from elements it has been embedded in, inhibiting hence its reliable retrieval from the original. In this paper, we adress attacks that can be modelled by an Additive White Gaussian Noise and Jitter (AWGN&J) channel in a game theory context. The AWGN&J channel was initially introduced to model local time fluctuations in the context of magnetic recording media. This channel is first briefly presented and characterized in terms of induced objective and perceptual distorsions. Also, performance loss of the one-bit watermarking Spread-Spectrum based scheme over an AWGN&J channel is derived. Then, results are applied in a game theoretic context to answer some questions such as: (i) for a given distortion budget, and from the attacker point of view, what part should be allocated to the desynchronization, and what part should be allocated to the additive noise?, (ii) from the defender point of view, what is the worst distortion? and (iii) is there means to countermeasure the attacker (limit the amount of objective distorsion)?