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Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

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  • Mark Broom

    (City, University of London)

  • Jan Rychtář

    (The University of North Carolina at Greensboro)

Abstract

The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a “predator dilution game” where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted.

Suggested Citation

  • Mark Broom & Jan Rychtář, 2018. "Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions," Dynamic Games and Applications, Springer, vol. 8(1), pages 79-92, March.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-016-0204-4
    DOI: 10.1007/s13235-016-0204-4
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    References listed on IDEAS

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    1. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    2. Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.
    3. Křivan, Vlastimil & Cressman, Ross & Schneider, Candace, 2008. "The ideal free distribution: A review and synthesis of the game-theoretic perspective," Theoretical Population Biology, Elsevier, vol. 73(3), pages 403-425.
    4. Bernhard Voelkl, 2010. "The ‘Hawk-Dove’ Game and the Speed of the Evolutionary Process in Small Heterogeneous Populations," Games, MDPI, vol. 1(2), pages 1-14, May.
    5. C. Hadjichrysanthou & M. Broom & J. Rychtář, 2011. "Evolutionary Games on Star Graphs Under Various Updating Rules," Dynamic Games and Applications, Springer, vol. 1(3), pages 386-407, September.
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    Cited by:

    1. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.

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