The price of anarchy, the most popular measure of the inefficiency 
of selfish behavior, assumes that players successfully 
reach some Nash equilibrium.  We prove that for most of the classes
of games in which the price of anarchy has been studied, results
are "intrinsically robust" in the following sense:
an upper bound on the worst-case price of anarchy for pure Nash
equilibria *necessarily* implies the exact same worst-case upper
bound for a much larger sets of outcomes, including mixed Nash equilibria, 
correlated equilibria, and sequences of outcomes generated by natural 
experimentation strategies (such as successive best responses or 
simultaneous regret-minimization).  Byproducts of our work include 
several new results for the inefficiency of equilibria in congestion 
games.