Vol. 10, No. 5, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Optimal aggression in kleptoparasitic interactions

David G. Sykes and Jan Rychtář

Vol. 10 (2017), No. 5, 735–747
Abstract

We have created and analyzed a model for kleptoparasitic interactions when individuals decide on the level of aggression in which they want to engage in the contest over a resource item. The more aggressive each individual is relative to an opponent, the higher are the chances of winning the item, but also the higher is the cost of the interaction for that individual. We consider a general class of cost functions and show that for any parameter values, i.e., for any maximal potential level of aggression of the individuals, any value of the resource and any type of the cost function, there is always a unique Nash equilibrium. We identify four possible kinds of Nash equilibria and give precise conditions for when they occur. We find that nonaggressive behavior is not a Nash equilibrium even when the cost function is such that aggressive behavior yields lower payoffs than avoiding the conflict altogether.

Keywords
kleptoparasitism, food stealing, game theory
Mathematical Subject Classification 2010
Primary: 91A05, 91A40
Milestones
Received: 14 August 2015
Revised: 25 July 2016
Accepted: 7 August 2016
Published: 14 May 2017

Communicated by Natalia Hritonenko
Authors
David G. Sykes
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
United States
Jan Rychtář
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27412
United States