This paper explores the application of event-based cameras in the domains of image segmentation and motion estimation. These cameras offer a groundbreaking technology by capturing visual information as a continuous stream of asynchronous events, departing from the conventional frame-based image acquisition. We introduce a Generalized Nash Equilibrium based framework that leverages the temporal and spatial information derived from the event stream to carry out segmentation and velocity estimation. To establish the theoretical foundations, we derive an existence criteria and propose a multi-level optimization method for calculating equilibrium. The efficacy of this approach is shown through a series of experiments.