Journal of Mathematical Biology

, Volume 32, Issue 6, pp 597–615

Sequential methods for generating patterns of ESS's

  • M. Broom
  • C. Cannings
  • G. T. Vickers
Article

DOI: 10.1007/BF00573463

Cite this article as:
Broom, M., Cannings, C. & Vickers, G.T. J. Math. Biology (1994) 32: 597. doi:10.1007/BF00573463

Abstract

A finite conflict with given payoff matrix may have many ESS's (evolutionarily stable strategies). For a given set of pure strategies { 1, 2, ...,n} a set of subsets of these is called a pattern, and if there exists ann ×n matrix which has ESS's whose supports (i.e. the playable strategies) precisely match the elements of the pattern, then the pattern is said to be attainable. In [5] and [10] some methods were developed to specify when a pattern was, or was not, attainable. The object here is to present a somewhat different method which is essentially recursive. We derive certain results which allow one to deduce from the attainability of a pattern for givenn the attainability of other patterns forn+1, and by induction for anyn+r.

Key words

PRIMARY 90D05SECONDARY 92A15ESSPatternsPolymorphism

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. Broom
    • 1
    • 2
  • C. Cannings
    • 1
  • G. T. Vickers
    • 2
  1. 1.School of Mathematics and Statistics, Division of Probability and StatisticsUniversity of SheffieldSheffieldUK
  2. 2.School of Mathematics and Statistics, Division of Applied and Computational MathematicsUniversity of SheffieldSheffieldUK