I found this explanation much clearer than the original post. Well done!
Everyone plays 99, unless someone defects [by the way this could be by playing 30, an action which literally helps everyone], in which case we play 100
This is indeed a very odd / unrealistic-seeming strategy profile. Consider a different, still weird but slightly more natural strategy profile:
Everyone plays 99, unless someone defects [which is defined as playing something higher than 99], in which case we play 100
This is not a Nash equilibrium, since any player can now do better by unilaterally lowering their own number. If the players start with this strategy profile, they probably quickly settle into the more natural Nash equilibrium of all playing 30.
It’s useful to remember that a Nash equilibrium is an equilibrium. Various real systems:
may not always be at equilibrium
may be nudged away from a particular equilibrium by a very small nudge, and then settle into a radically different equilibrium pretty quickly thereafter.
I found this explanation much clearer than the original post. Well done!
This is indeed a very odd / unrealistic-seeming strategy profile. Consider a different, still weird but slightly more natural strategy profile:
This is not a Nash equilibrium, since any player can now do better by unilaterally lowering their own number. If the players start with this strategy profile, they probably quickly settle into the more natural Nash equilibrium of all playing 30.
It’s useful to remember that a Nash equilibrium is an equilibrium. Various real systems:
may not always be at equilibrium
may be nudged away from a particular equilibrium by a very small nudge, and then settle into a radically different equilibrium pretty quickly thereafter.