Research Article
Competition between foraging predators and hiding preys as a nonzero-sum differential game
@INPROCEEDINGS{10.1109/GAMENETS.2009.5137421, author={Andrei R. Akhmetzhanov and Pierre Bernhard and Frederic Grognard and Ludovic Mailleret}, title={Competition between foraging predators and hiding preys as a nonzero-sum differential game}, proceedings={1st International Conference on Game Theory for Networks}, publisher={IEEE}, proceedings_a={GAMENETS}, year={2009}, month={6}, keywords={}, doi={10.1109/GAMENETS.2009.5137421} }- Andrei R. Akhmetzhanov
Pierre Bernhard
Frederic Grognard
Ludovic Mailleret
Year: 2009
Competition between foraging predators and hiding preys as a nonzero-sum differential game
GAMENETS
IEEE
DOI: 10.1109/GAMENETS.2009.5137421
Abstract
In this work we investigate a (seasonal) prey-predator model where the system evolves during a season whose length is fixed. Predators have the choice between foraging the food (eating preys) and reproducing (laying eggs at a rate proportional to their energy). Preys can either eat, which would maintain their population in the absence of predators, or hide from the predators but they then suffer a positive mortality rate. In this case the population size can decrease even faster than if they were not hiding and were foraged by the predators. In their own turn they lay eggs at a constant rate whether they are hiding or eating. Following Darwin's principle that the fittest population will survive we postulate that both populations must maximize the number of their offspring, which yields a nonzero-sum differential game.