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The Hawk–Dove game as an average-cost problem

Published online by Cambridge University Press:  01 July 2016

J. M. McNamara ,
S. Merad  and
E. J. Collins
J. M. McNamara
Affiliation:
University of Bristol
S. Merad
Affiliation:
University of Bristol
E. J. Collins*
Affiliation:
University of Bristol
*
∗Postal address for all authors: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
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Abstract

This paper considers a version of the Hawk–Dove game of Maynard Smith and Price (1973) in which animals compete for a sequence of food items. Actions may depend on an animal's energy reserves. Costs and transition probabilities under a given policy depend on the mean level of aggressiveness, p, of the rest of the population. We find the optimal policy for a single animal under an average cost criterion when ρ is constant over time. We then consider the whole interacting population when individual members follow the same stationary policy. It is shown that the mean aggressiveness, p, asymptotically approaches a limiting value in this population. We then consider the existence of evolutionarily stable strategies for the population. It is shown that such strategies always exist but may not be unique.

Keywords

INTERACTING POPULATIONEVOLUTIONARILY STABLE STRATEGIESAVERAGE-COST OPTIMALITY
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 667 - 682
Copyright
Copyright © Applied Probability Trust 1991 

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References

Grafen, A. (1987) The logic of divisively asymmetric contests: respect for ownership and the desperado effect. Anim. Behav. 35, 462–467.Google Scholar
Houston, A. I. and Mcnamara, J. M. (1988) Fighting for food: a dynamic version of the Hawk–Dove game. Evolutionary Ecology 2, 51–64.Google Scholar
Houston, A. I. and Mcnamara, J. M. (1991) Evolutionarily stable strategies in the repeated Hawk–Dove game. Behavioural Ecology. To appear.Google Scholar
Mcnamara, J. M. (1990) The policy which maximises long-term survival of an animal faced with the risks of starvation and predation. Adv. Appl. Prob. 22, 295–308.Google Scholar
Maynard Smith, J. (1982) Evolution and the Theory of Games. Cambridge University Press.CrossRefGoogle Scholar
Maynard Smith, J. and Price, G. R. (1973) The logic of animal conflict. Nature 246, 15–18.Google Scholar
Whittle, P. (1983) Optimization over Time , Vol II. Wiley, Chichester.Google Scholar