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

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 90D05 SECONDARY 92A15 ESS Patterns Polymorphism 

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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

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