IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v208y2011i2p131-141.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00537-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. N. Zoroa & M. J. Fernández-Sáez & P. Zoroa, 2004. "Search and Ambush Games with Capacities," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 431-450, November.
    4. 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.
    5. 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.
    6. 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.
    7. Hohzaki, Ryusuke, 2006. "Search allocation game," European Journal of Operational Research, Elsevier, vol. 172(1), pages 101-119, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vicki Bier & Naraphorn Haphuriwat, 2011. "Analytical method to identify the number of containers to inspect at U.S. ports to deter terrorist attacks," Annals of Operations Research, Springer, vol. 187(1), pages 137-158, July.
    2. Hohzaki, Ryusuke & Maehara, Hiroki, 2010. "A single-shot game of multi-period inspection," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1410-1418, December.
    3. Deutsch, Yael & Golany, Boaz & Rothblum, Uriel G., 2011. "Determining all Nash equilibria in a (bi-linear) inspection game," European Journal of Operational Research, Elsevier, vol. 215(2), pages 422-430, December.
    4. Naraphorn Haphuriwat & Vicki M. Bier & Henry H. Willis, 2011. "Deterring the Smuggling of Nuclear Weapons in Container Freight Through Detection and Retaliation," Decision Analysis, INFORMS, vol. 8(2), pages 88-102, June.
    5. Fandel, G. & Trockel, J., 2013. "Avoiding non-optimal management decisions by applying a three-person inspection game," European Journal of Operational Research, Elsevier, vol. 226(1), pages 85-93.
    6. Deutsch, Yael, 2021. "A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1036-1052.
    7. Safaei, Mehdi, 2014. "An integrated multi-objective model for allocating the limited sources in a multiple multi-stage lean supply chain," Economic Modelling, Elsevier, vol. 37(C), pages 224-237.
    8. Stamatios Katsikas & Vassili Kolokoltsov & Wei Yang, 2016. "Evolutionary Inspection and Corruption Games," Games, MDPI, vol. 7(4), pages 1-25, October.
    9. Ryusuke Hohzaki, 2008. "A search game taking account of attributes of searching resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 76-90, February.
    10. Puneet Agarwal & Kyle Hunt & Shivasubramanian Srinivasan & Jun Zhuang, 2020. "Fire Code Inspection and Compliance: A Game-Theoretic Model Between Fire Inspection Agencies and Building Owners," Decision Analysis, INFORMS, vol. 17(3), pages 208-226, September.
    11. Vassili Kolokoltsov, 2017. "The Evolutionary Game of Pressure (or Interference), Resistance and Collaboration," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 915-944, November.
    12. Nourinejad, Mehdi & Gandomi, Amir & Roorda, Matthew J., 2020. "Illegal parking and optimal enforcement policies with search friction," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    13. Owen Q. Wu & Volodymyr Babich, 2012. "Unit-Contingent Power Purchase Agreement and Asymmetric Information About Plant Outage," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 245-261, April.
    14. Chen-Kuo Pai & Tingting Lee & Sangguk Kang, 2021. "Examining the Role of Service Quality, Perceived Values, and Trust in Macau Food Festival," IJERPH, MDPI, vol. 18(17), pages 1-16, September.
    15. Ryusuke Hohzaki, 2009. "A cooperative game in search theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 264-278, April.
    16. Huijie Li & Deqing Tan, 2024. "How to Control Waste Incineration Pollution? Cost-Sharing or Penalty Mechanism—Based on Two Differential Game Models," Decision Analysis, INFORMS, vol. 21(2), pages 91-109, June.
    17. Dong, Xiaoqing & Li, Chaolin & Li, Ji & Wang, Jia & Huang, Wantao, 2010. "A game-theoretic analysis of implementation of cleaner production policies in the Chinese electroplating industry," Resources, Conservation & Recycling, Elsevier, vol. 54(12), pages 1442-1448.
    18. Tzavara Dionisia & Heritier Adrienne, 2012. "Quality and Environmental Regulation: Verifying Compliance along the Supply Chain," Business and Politics, De Gruyter, vol. 14(2), pages 1-24, August.
    19. Zhang, Manman & Zhang, Juliang & Sun, Yue & Cheng, T.C.E., 2022. "How to outsource production considering quality management: Turnkey or buy-sell?," Omega, Elsevier, vol. 113(C).
    20. Liu, Guanmei & Shao, Xiaofeng & Lang, Xiao, 2020. "On the interaction of technology upgrade and buyer entry in a supply chain," International Journal of Production Economics, Elsevier, vol. 221(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:131-141. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.