This paper presents a preliminary study into the use of collision cones in analyzing pursuit evasion games between two objects of arbitrary shapes. A two-player pursuit evasion game is considered, wherein a single pursuer tries to capture a single evader who, in turn, tries to avoid capture. The collision cone is defined as the set of instantaneous velocities that cause one player to lie on a collision course with the other. The evader applies an acceleration to drive the relative velocity vector out of the collision cone, while the pursuer applies an acceleration to drive the relative velocity vector into the collision cone. Two different matrix games are considered, and saddle points (defined by the scenarios wherein the relative velocity vector is aligned with the boundary of the collision cone at the instant of closest approach) are determined.