We propose a game-theoretic model analyzing the interaction between the State and any possible relative taxpayer, by using a realistic probability (frequency) approach to the checking evasion strategy. Starting from Allingham and Sandmo's model (1972), we study a possible measure to prevent tax evasion and we also propose a "honesty-award" for Taxpayers declaring their entire income by using two Kalai-Smorodinsky solutions. This methodology leaves room for further development of the model, leading to a self-identification by tax evaders and honest citizens.