Predator-prey systems are ubiquitous across ecological systems. Typical ecological models focus on the dynamics of predator-prey populations. Eco-evolutionary models integrate arms race or Red-Queen like dynamics. The roles of the predator and prey species are always assumed to be static. Nevertheless, sometimes predators can bite off more than they can chew. For example, predators that encounter multiple or dangerous prey types may need to develop new predatory tactics to capture prey. We explore the dynamics of predator-prey dynamics when the prey can injure or kill the predator. This common ecological scenario places pressure on the predator to develop novel predatory tactics to both capture prey and avoid counter-attack from prey. Taking a bottom-up approach, we develop the Holling function mechanistically and then implement it in a model of innovationselection dynamics inspired by economic theory. We show how an interdisciplinary approach can be used to explain the emergence of complex predatory behaviours. Notably, our study shows why predators may hunt dangerous prey even when safe prey are available. In a broader context, we demonstrate how a multidisciplinary approach combining ecology, evolution and economics improves our understanding of a complex behavioural trait.