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 x 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.