Patterns of evolutionarily stable strategies: the maximal pattern conjecture revisited

A conflict is defined by a set of pure strategies [1,..., n] and a payoff matrix, and may have many evolutionarily stable strategies (ESSs). A collection of subsets of the set of pure strategies is called a pattern. If there is an n x n matrix which has ESSs whose supports match those of the pattern, then that pattern is said to be attainable. Much of the work on patterns of ESSs relied upon an unproved conjecture. Subject to some relaxation of the definition of attainability, this conjecture is proved.