A generalized war of attrition
Abstract
In the "War of Attrition" model of animal conflict, introduced by Maynard Smith, a reward is obtained by whichever of two opponents displays longer, each individual incurring a cost associated with the length of the contest. This model is generalized to allow more general reward and cost functions, and restrictions on the length of contest permitted. This permits unification of the "War of Attrition" model and the "Graduated Risks" model, and also the extension to models in which contests may end either due to injury, or to retreat.
In each case it is demonstrated that either (i) there is no evolutionary stable strategy (ESS) or (ii) there is a unique ESS, which is fully specified. In the case where only a finite number of pure strategies are available, global convergence to the ESS is shown. A variety of interesting conclusions of biological relevance emerge, perhaps the most striking being the occurrence of a dichotomous behavioural pattern in an essentially continuous conflict.- Publication:
-
Journal of Theoretical Biology
- Pub Date:
- 1978
- DOI:
- 10.1016/0022-5193(78)90304-1
- Bibcode:
- 1978JThBi..70...85B