  The Le Chatelier principle states that physical equilibria are not only
stable, but they also resist external perturbations via short-time
negative-feedback mechanisms: a perturbation induces processes tending to
diminish its results. The principle has deep roots, e.g., in thermodynamics it
is closely related to the second law and the positivity of the entropy
production. Here we study the applicability of the Le Chatelier principle to
evolutionary game theory, i.e., to perturbations of a Nash equilibrium within
the replicator dynamics. We show that the principle can be reformulated as a
majorization relation. This defines a stability notion that generalizes the
concept of evolutionary stability. We determine criteria for a Nash equilibrium
to satisfy the Le Chatelier principle and relate them to mutualistic
interactions (game-theoretical anticoordination) showing in which sense
mutualistic replicators can be more stable than (say) competing ones. There are
globally stable Nash equilibria, where the Le Chatelier principle is violated
even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium
can amplify small perturbations, though both this type of equilibria satisfy
the detailed balance condition.
