Combinatorial Aspects of Parker’s Model

Parker’s model under rare mutation is considered when there is a finite set of available strategies. The question of when all of those strategies are present in the stationary distribution, i.e., the Markov chain is irreducible, is addressed, via graph theoretic and combinatorial entities. Specific...

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Bibliographic Details
Published inDynamic games and applications Vol. 5; no. 2; pp. 263 - 274
Main Author Cannings, Chris
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2015
Subjects
Communications Engineering
Computer Systems Organization and Communication Networks
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Game Theory
Management Science
Mathematics
Mathematics and Statistics
Networks
Operations Research
Social and Behav. Sciences
Evolutionarily stable strategy (ESS)
Dyck words
Catalan numbers
Parker’s model
Irreducible
Stationary distribution
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Summary:Parker’s model under rare mutation is considered when there is a finite set of available strategies. The question of when all of those strategies are present in the stationary distribution, i.e., the Markov chain is irreducible, is addressed, via graph theoretic and combinatorial entities. Specific cases for n = 3 , 4 , 5 , 6 are addressed, in the first three cases all the feasible cases are specified, and for n = 6 a superset of the feasible cases (possibly the set itself) is given.
ISSN:2153-0785
2153-0793
DOI:10.1007/s13235-014-0103-5