Talk:Evolutionarily stable state

Should this just be a redirect to Evolutionarily stable strategy? I always used the terms interchangeably. ~ trialsanderrors 08:56, 9 February 2007 (UTC)[reply]

I don't think the terms are synonymous (though I do acknowledge that many people do use them interchangeably). I seem to remember some discussion about this c. mid 2005 reflected in the Evolutionarily_stable_strategy#ESS_vs._Evolutionarily_Stable_State section. Briefly I think ESS is a Nash equil. refinement (meets JMS '82 definition), while an ES State is a (closely related) EGT-style population state. A redirect to the ESS#ESS_vs._Evolutionarily_Stable_State section would be more appropriate than a straight redirect to ESS. Pete.Hurd 15:09, 9 February 2007 (UTC)[reply]

I agree with Pete about this. Polymorphic stable points in the replicator dynamics (like the global attractor in the one population model of chicken (game)) are appropriately called evolutionarily stable states. But in that model neither hawk nor dove are evolutionarily stable strategies (they can both be invaded). I think Hofbauer and Sigmund define evolutionary stable state akin to the way an attractor is defined in dynamical systems (there is an epsilon neighborhood which converges to the state). --best, kevin [kzollman][talk] 18:47, 9 February 2007 (UTC)[reply]

Oh, OK. Makes me wonder if stochastically stable equilibrium is really an ESS refinement, even though it's defined as such in Foster & Young. I'll have to read up on it. ~ trialsanderrors 19:54, 9 February 2007 (UTC)[reply]

There is a stochastic concept of ESS called ESS_N that is used by Nowak and others. See the book "Evolutionary Dynamics" by Nowak. The subscript indicates that evolutionary stability is dependent on the population size.—Preceding unsigned comment added by Marc Harper (talk • contribs)