Paul Samuelson’s critique and equilibriumconcepts in evolutionary game theory

We present two new notions of evolutionary stability, the trulyevolutionarily stable state (TESS) and the generalized evolutionarilystable equilibrium (GESE). The GESE generalizes the evolutionar-ily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts allnearby trajectories monotonically, i.e., the Euclidean distance decreas-ing steadily in time. For a GESE this property should holds for at leastone metric. The TESS generalizes the evolutionarily stable strategy(ESS) of Maynard Smith & Price [1973]. A TESS attracts nearby tra-jectories too, but the behavior of the dynamics nearby must be similarto the behavior of the replicator dynamics near an ESS.[...]