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A foraging problem: Sit-and-wait versus active predation

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  • Zoroa, N.
  • Fernández-Sáez, M.J.
  • Zoroa, P.

Abstract

The literature on foraging shows that some predators use a combination of ambush and active search to locate a prey. Let us suppose that a prey must go every day to some determined places to feed, and to another place, 0, to drink. A predator can stay at zone 0 waiting for the prey (sit-and-wait strategy) or it can move between the different places where the prey will go to eat (search strategy). If predator and prey meet each other in the same place, prey will be caught with a probability depending on the place. We study this problem in different situations, modelling them as two-person zero-sum games. We solve them in closed form, giving optimal strategies for prey and for predator and the value of the games.

Suggested Citation

  • Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2011. "A foraging problem: Sit-and-wait versus active predation," European Journal of Operational Research, Elsevier, vol. 208(2), pages 131-141, January.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:131-141
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    References listed on IDEAS

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    1. Avenhaus, Rudolf & Canty, Morton & Marc Kilgour, D. & von Stengel, Bernhard & Zamir, Shmuel, 1996. "Inspection games in arms control," European Journal of Operational Research, Elsevier, vol. 90(3), pages 383-394, May.
    2. Hsieh, Chung-Chi & Liu, Yu-Te, 2010. "Quality investment and inspection policy in a supplier-manufacturer supply chain," European Journal of Operational Research, Elsevier, vol. 202(3), pages 717-729, May.
    3. Zoroa, N. & Zoroa, P. & Fernández-Sáez, M.J., 2009. "Weighted search games," European Journal of Operational Research, Elsevier, vol. 195(2), pages 394-411, June.
    4. Avenhaus, Rudolf & Canty, Morton John, 2005. "Playing for time: A sequential inspection game," European Journal of Operational Research, Elsevier, vol. 167(2), pages 475-492, December.
    5. Chris L. Higgins & Richard E. Strauss, 2004. "Discrimination and classification of foraging paths produced by search-tactic models," Behavioral Ecology, International Society for Behavioral Ecology, vol. 15(2), pages 248-254, March.
    6. Hohzaki, Ryusuke, 2006. "Search allocation game," European Journal of Operational Research, Elsevier, vol. 172(1), pages 101-119, July.
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    Cited by:

    1. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    2. Noemí Zoroa & María-José Fernández-Sáez & Procopio Zoroa, 2015. "Ambush and Active Search in Multistage Predator–Prey Interactions," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 626-643, August.
    3. Alpern, Steve & Fokkink, Robbert & Simanjuntak, Martin, 2016. "Optimal search and ambush for a hider who can escape the search region," European Journal of Operational Research, Elsevier, vol. 251(3), pages 707-714.

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