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This article explains differential games—a continuous‑time game‑theoretic framework—by outlining its core components, presenting a predator‑prey case study, and showing simulation results that illustrate how optimal control strategies emerge in dynamic ecological interactions.
During World War I, shark catches rose sharply, prompting biologist D. Ancona to enlist mathematician Volterra, whose differential‑equation predator‑prey model—later extended with a logistic term—explains the disproportionate increase of sharks by accounting for fishing pressure and natural population dynamics.
The article explains the classic Volterra predator‑prey differential equations, derives the basic model, shows how adding a logistic term captures realistic population limits, and demonstrates how wartime fishing reductions lead to a disproportionate increase in shark numbers, illustrating the model’s explanatory power.