Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T12:00:48.952Z Has data issue: false hasContentIssue false
  • English
  • Français

The allocation of resources in a multiple-trial war of attrition conflict

Published online by Cambridge University Press:  01 July 2016

J. C. Whittaker
J. C. Whittaker*
Affiliation:
University of Reading
*
∗ Postal address: Department of Applied Statistics, University of Reading, Reading RG32AL, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a model in which players must divide a fixed amount of resource between a number of trials of an underlying contest, with the underlying contest based on the War of Attrition. We are able to find the unique ES set (a simple generalisation of the idea of an evolutionarily stable strategy) in certain circumstances: in particular we find the conditions under which the ES set may contain a pure strategy.

Keywords

EVOLUTIONARILY STABLE STRATEGIESFINITE CONFLICTSGAME THEORY
Type
General Applied Probablity
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996 , pp. 933 - 964
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Beale, E. M. L. and Heselden, G. P. ?. (1962) An approximate method of solving Blotto games. Naval Res. Log. Quart. 9, 65–79.Google Scholar
[2] Bishop, D. T. and Cannings, C. (1976) Models of animal conflict. Adv. Appl. Prob. 8, 616–621.Google Scholar
[3] Bishop, D. T. and Cannings, C. (1978) A generalised war of attrition. J. Theor. Biol. 70, 85–124.Google Scholar
[4] Blackett, D. W. (1958) Pure strategy solutions to Blotto games. Naval Res. Log. Quart. 5, 107–109.Google Scholar
[5] Cannings, C. and Whittaker, J. C. (1991) A two-trial two-strategy conflict. J. Theor. Biol. 149, 281–286.Google Scholar
[6] Maynard-Smith, J. and Price, G. R. (1973) The logic of animal conflicts. Nature 246, 15–18.Google Scholar
[7] Owen, G. (1982) Game Theory. 2nd edn. Academic Press, New York.Google Scholar
[8] Parker, G. A. (1990) Sperm competition games: sneaks and extra-pair copulations. Proc. R. Soc. London B 242, 127–133.Google Scholar
[9] Thomas, B. (1985) On evolutionary stable sets. J. Math. Biol. 22, 105–115.Google Scholar
[10] Thomas, B. (1985) Evolutionary sets in mixed strategist models. Theor. Pop. Biol. 28, 332–341.Google Scholar
[11] TuKey, J. W. (1949) A problem of strategy. Econometrica 17, 73.Google Scholar
[12] Whittaker, J. C. and Cannings, C. (1994) A resource allocation problem. J. Theor. Biol. 167, 397–405.Google Scholar
[13] Whittaker, J. C. and Cannings, C. (1994) Multiple trial two strategy conflicts. J. Theor. Biol. 169, 113–124.Google Scholar