  It is known that there are uncoupled learning heuristics leading to Nash
equilibrium in all finite games. Why should players use such learning
heuristics and where could they come from? We show that there is no uncoupled
learning heuristic leading to Nash equilibrium in all finite games that a
player has an incentive to adopt, that would be evolutionary stable or that
could "learn itself". Rather, a player has an incentive to strategically teach
such a learning opponent in order secure at least the Stackelberg leader
payoff. The impossibility result remains intact when restricted to the classes
of generic games, two-player games, potential games, games with strategic
complements or 2x2 games, in which learning is known to be "nice". More
generally, it also applies to uncoupled learning heuristics leading to
correlated equilibria, rationalizable outcomes, iterated admissible outcomes,
or minimal curb sets. A possibility result restricted to "strategically
trivial" games fails if some generic games outside this class are considered as
well.
