Evolutionarily stable strategy
A way of behaving that, once almost everyone in a population follows it, cannot be displaced by a small group behaving differently.
Often misread asTreating ESS as Nash equilibrium renamed for biologists, so any symmetric Nash equilibrium of the game gets called evolutionarily stable.
How to see it
Stable against the mutant that could appear, not just best against itself
A strategy is evolutionarily stable if a whole population playing it cannot be invaded by a small group playing something else. The test is not whether the strategy does well on average, it is whether a rare mutant doing something different would spread. If the mutant earns less than the residents while it is still rare, the resident strategy holds.
The checkESS is Nash plus a tie-breaker: when a mutant does exactly as well against the resident as the resident does against itself, the resident must do strictly better against the mutant than the mutant does against its own kind. Every ESS is Nash, but not every symmetric Nash is an ESS.
Try itFind a symmetric game in which some strategy is only a weak best response to itself. Check what happens when the tying mutant meets a copy of itself. If it does better in that meeting than the resident does against it, you have a symmetric Nash equilibrium that is not an ESS.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Maynard Smith, J. & Price, G. (1973). Nature 246, 15-18.
- Maynard Smith, J. (1982). Cambridge University Press.