  It is shown in recent studies that in a Stackelberg game the follower can
manipulate the leader by deviating from their true best-response behavior. Such
manipulations are computationally tractable and can be highly beneficial for
the follower. Meanwhile, they may result in significant payoff losses for the
leader, sometimes completely defeating their first-mover advantage. A warning
to commitment optimizers, the risk these findings indicate appears to be
alleviated to some extent by a strict information advantage the manipulations
rely on. That is, the follower knows the full information about both players'
payoffs whereas the leader only knows their own payoffs. In this paper, we
study the manipulation problem with this information advantage relaxed. We
consider the scenario where the follower is not given any information about the
leader's payoffs to begin with but has to learn to manipulate by interacting
with the leader. The follower can gather necessary information by querying the
leader's optimal commitments against contrived best-response behaviors. Our
results indicate that the information advantage is not entirely indispensable
to the follower's manipulations: the follower can learn the optimal way to
manipulate in polynomial time with polynomially many queries of the leader's
optimal commitment.
