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A dynamic programming approach to evolutionarily stable strategy theory

Published online by Cambridge University Press:  01 July 2016

C. Cannings
Affiliation:
University of Sheffield
D. Gardiner
Affiliation:
University of Sheffield

Extract

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

Type
Symposium on Mathematical Genetics, London, 26–27 March 1979
Copyright
Copyright © Applied Probability Trust 1980 

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References

Bishop, D. T. and Cannings, C. (1978) A generalized war of attrition. J. Theoret. Biol. 70, 85124.CrossRefGoogle ScholarPubMed
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209221.CrossRefGoogle Scholar