Journal of Mathematical Biology

, Volume 76, Issue 1–2, pp 457–482 | Cite as

The effect of fight cost structure on fighting behaviour involving simultaneous decisions and variable investment levels

  • Mark Broom
  • Michal Johanis
  • Jan Rychtář


In the “producer–scrounger” model, a producer discovers a resource and is in turn discovered by a second individual, the scrounger, who attempts to steal it. This resource can be food or a territory, and in some situations, potentially divisible. In a previous paper we considered a producer and scrounger competing for an indivisible resource, where each individual could choose the level of energy that they would invest in the contest. The higher the investment, the higher the probability of success, but also the higher the costs incurred in the contest. In that paper decisions were sequential with the scrounger choosing their strategy before the producer. In this paper we consider a version of the game where decisions are made simultaneously. For the same cost functions as before, we analyse this case in detail, and then make comparisons between the two cases. Finally we discuss some real examples with potentially variable and asymmetric energetic investments, including intraspecific contests amongst spiders and amongst parasitoid wasps. In the case of the spiders, detailed estimates of energetic expenditure are available which demonstrate the asymmetric values assumed in our models. For the wasps the value of the resource can affect the probabilities of success of the defender and attacker, and differential energetic investment can be inferred. In general for real populations energy usage varies markedly depending upon crucial parameters extrinsic to the individual such as resource value and intrinsic ones such as age, and is thus an important factor to consider when modelling.


Kleptoparasitism Food stealing Producer–scrounger Game theory Simultaneous decisions 

Mathematics Subject Classification

91A05 92D50 



M. Johanis was supported by the grant GAČR and GAČR 16-07378S. J. Rychtář was supported by the Simons Foundation Grant 245400.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsCity, University of LondonLondonUK
  2. 2.Department of Mathematical AnalysisCharles UniversityPrague 8Czech Republic
  3. 3.Department of Mathematics and StatisticsThe University of North Carolina at GreensboroGreensboroUSA

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