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 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.