We consider strategic communication between two agents: a sender (S)-- the deceiver agent, and a  receiver (R). S has access two kinds of statistical information, state and private variables, while R aims to estimate the state. The objective  S is to render the state estimate of R  to be biased. While this problem has recently been considered in its original form, we now study an extension where the estimated distribution of the state at the receiver is different from the actual distribution. We characterize the optimal communication strategies and  the additional gain that the deceiver (S) can obtain using the mismatch in the state belief of R, for the case of Gaussian variables and quadratic distortions. For the case of non-Gaussian state, we obtain bounds to the aforementioned gain using the I-MMSE relations of Guo-Shamai-Verdu  and excess MMSE-divergence relations of Verdu. We make connections between this problem and the popular problem scenarios involving prospect-theoretic analysis of human behavior and the security of cyber-physical systems under advanced persistent threats.