This paper derives closed-form solutions for a strategic, simultaneous harvesting in a predator-prey system. Using a parametric constraint, it establishes the existence and uniqueness of a linear feedback-Nash equilibrium involving two specialized fleets and allow for continuous time results for a class of payoffs that have constant elasticity of the marginal utility. Theses results contribute to the scarce literature on analytically tractable predator-prey models with endogenous harvesting. A discussion based on industry size effects is provided to highlight the role played by biological versus strategic interactions in the multi-species context.