DOES NEUTRAL STABILITY IMPLY LYAPUNOV STABILITY

A central concept in evolutionary game theory is that of an evolutiona rily stable strategy. However, many games of interest for economics ha ve only strategies which meet the weaker requirement of neutral stabil ity. While neutral stability implies Lyapunov stability under the repl icator dynamics in pairwise interactions, we give here an example in w hich an evolutionarily stable strategy is not Lyapunov stable in a mor e general context. We propose to use instead the notions of (strong) u ninvadability and (strong) unbeatability, refinements of evolutionary and neutral stability, respectively. Strong uninvadability implies asy mptotic stability, and strong unbeatability implies Lyapunov stability under the replicator dynamics. (C) 1995 Academic Press, Inc.