In this paper, we derive a non-zero-sum multi-player game that models pursuit-evasion tactics in an acoustic field. Specifically, the Pursuer uses acoustic sensing to determine the location of the Evader. However, this sensing ability is corrupted by noise generated from the motion of both the Pursuer and Evader. It is argued that the dominant mechanism of sensory degrading noise from the Pursuer is a function of speed, while the noise from the Evader is a function of acceleration and speed. Depending on the set of parameters characterizing the game, the control evolution exhibits various striking and diverse qualitative features. In some cases, the strategy of choosing actions associated with one step Nash equilibria yields a limit cycle response. This confirms observations by other researchers that the temporal evolution of games need not converge to a single Nash equilibrium and opens opportunities for future analysis on making the correct choice of cost functions by determining the effects this has on the agent's ability to obtain a desired goal.