Abstract
In this paper, we study a multistage search game. The general situation is described as a predator–prey problem as follows: in a certain region there is a predator and a group of prey. The prey have h different places to go to eat, and every day the group goes to one of these places, but all the days, the herd is forced to go to a certain place, W, say to drink. Simultaneously, the predator has to select a strategy to meet the herd of prey and catch one of them, it can use its ambush strategy, which consists of going to place W, and wait there for the herd, or select a search strategy and go to one of the h different places where the herd goes to eat and search for a prey there. When predator and prey meet each other in one place, predator can catch a prey with a probability depending on the place and on the movement of the predators. Since animals require a minimum consumption of energy over time to survive, we suppose that the predator has to catch a minimum number of prey, K, over a number of days, M. We model this problem as a two-person zero-sum multistage game, which we solve in some situations by giving optimal strategies for prey and for predator and the value of the game.
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Acknowledgments
This research has been supported by the Fundación Séneca of the Comunidad Autónoma de la Región de Murcia, Project 08716/ PI/08. The authors thank an anonymous referee and the editor for their constructive comments, which have greately improved the paper, and they thank Pascual Lucas and Josefa Marín for their very helpful suggestions.
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Communicated by Negash G. Medhin.
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Zoroa, N., Fernández-Sáez, MJ. & Zoroa, P. Ambush and Active Search in Multistage Predator–Prey Interactions. J Optim Theory Appl 166, 626–643 (2015). https://doi.org/10.1007/s10957-014-0620-9
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DOI: https://doi.org/10.1007/s10957-014-0620-9