Diel Vertical Migration (DVM), the daily movement of organisms through oceanic water columns, is mainly driven by spatio-temporal variations in light affecting the intensity of predator-prey interactions. Migration patterns of an organism are intrinsically linked to the distribution of its conspecifics, its prey, and its predators, each with their own fitness seeking imperatives. We present a mechanistic, trait-based model of DVM for the different components of a pelagic community. Specifically we consider size, sensory mode, and feeding mode as key traits, representing a community of copepods that prey on each other and are, in turn, preyed upon by fish. Using game theoretic principles, we explore the optimal distribution of the main groups of a planktonic pelagic food-web simultaneously. Within one single framework, our model reproduces a whole suite of observed patterns, such as size-dependent DVM patterns of copepods and reverse migrations. These patterns can only be reproduced when different trophic levels are considered at the same time. This study facilitates a quantitative understanding of the drivers of DVM, and is an important step towards mechanistically underpinned predictions of DVM patterns and biologically mediated carbon export.