Some remarks on evolutionary stability in matrix games

In this article, we revisit evolutionary stability in matrix games. We provide a new direct proof to characterize a pure evolutionarily stable strategy (ESS), in games with exactly two pure strategies, as a strategy that is evolutionarily stable against multiple mutations. This direct proof yields generalizations to k × k games which explains why such a characterization is not possible in general. Furthermore, we prove other necessary/sufficient conditions for evolutionary stability against multiple mutations. © 2013 World Scientific Publishing Company.