Geodesic
Kleptoparasitic Interactions under Asymmetric Resource Valuation
M. Broom1 ; J. Rychtář2 ; D. Sykes2
1 Department of Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, UK
2 Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC 27402, USA
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 3, pp. 138-147

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We introduce a game theoretical model of stealing interactions. We model the situation as an extensive form game when one individual may attempt to steal a valuable item from another who may in turn defend it. The population is not homogeneous, but rather each individual has a different Resource Holding Potential (RHP). We assume that RHP not only influences the outcome of the potential aggressive contest (the individual with the larger RHP is more likely to win), but that it also influences how an individual values a particular resource. We investigate several valuation scenarios and study the prevalence of aggressive behaviour. We conclude that the relationship between RHP and resource value is crucial, where some cases lead to fights predominantly between pairs of strong individuals, and some between pairs of weak individuals. Other cases lead to no fights with one individual conceding, and the order of strategy selection is crucial, where the individual which picks its strategy first often has an advantage.
DOI : 10.1051/mmnp/20149309

M. Broom 1 ; J. Rychtář 2 ; D. Sykes 2

1 Department of Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, UK
2 Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC 27402, USA 
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M. Broom; J. Rychtář; D. Sykes. Kleptoparasitic Interactions under Asymmetric Resource Valuation. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 3, pp. 138-147. doi: 10.1051/mmnp/20149309

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