Desensitization addresses safe optimal planning under parametric uncertainties by providing sensitivity function-based risk estimates. This paper expands upon the existing work on desensitization in optimal control to address safe planning for a class of two-player differential games. In the proposed game, parametric uncertainties correspond to variations of the model parameters for each player about their nominal values. The two players in the proposed formulation are assumed to have perfect information about these nominal parameter values. However, it is assumed that only one of the players has complete knowledge of the actual parameter value, resulting in information asymmetry in the proposed game. This lack of knowledge regarding the parameter variations is expected to result in state constraint violations for the player with an information disadvantage. In this regard, a desensitized feedback strategy that provides safe trajectories is proposed for the player with incomplete information. The proposed feedback strategy is evaluated for instances involving a single pursuer and a single evader with an uncertain moving obstacle, where the pursuer is assumed to only know the nominal value of the obstacle's speed. At the same time, the evader knows the obstacle's true speed, and also the fact that the pursuer knows only the nominal value of the obstacle's speed. Subsequently, deceptive strategies are proposed for the evader, who has an information advantage, and these strategies are assessed against the pursuer's desensitized strategy.