ESS PATTERNS - ADDING PAIRS TO AN ESS

The notion of a pattern of evolutionarily stable strategies was introd uced by Cannings and Vickers in 1988 (J. Theor. Biol. 132:387-420). In this paper a specific class of patterns is considered. Suppose that t here is an evolutionarily stable strategy (ESS) on some set of n strat egies {1,2,..., n} and that new strategies {n+1, n+2,..., n+k} are add ed. Supposing that for this new enlarged conflict there is still an ES S on {1,2,..., n} and also that there are ESSs on {n+i, j} for 1 less than or equal to i less than or equal to k and j is an element of S-i subset of {1, 2,..., n}, the authors investigate the restrictions on t he S-i. These restrictions are related to certain properties of strong tournaments introduced by Reid and Beineke. We also specify, given th e S-i, what ESSs of the form {n+i, n+j} can be added.