  Information uncertainty is one of the major challenges facing applications of
game theory. In the context of Stackelberg games, various approaches have been
proposed to deal with the leader's incomplete knowledge about the follower's
payoffs, typically by gathering information from the leader's interaction with
the follower. Unfortunately, these approaches rely crucially on the assumption
that the follower will not strategically exploit this information asymmetry,
i.e., the follower behaves truthfully during the interaction according to their
actual payoffs. As we show in this paper, the follower may have strong
incentives to deceitfully imitate the behavior of a different follower type
and, in doing this, benefit significantly from inducing the leader into
choosing a highly suboptimal strategy. This raises a fundamental question: how
to design a leader strategy in the presence of a deceitful follower? To answer
this question, we put forward a basic model of Stackelberg games with
(imitative) follower deception and show that the leader is indeed able to
reduce the loss due to follower deception with carefully designed policies. We
then provide a systematic study of the problem of computing the optimal leader
policy and draw a relatively complete picture of the complexity landscape;
essentially matching positive and negative complexity results are provided for
natural variants of the model. Our intractability results are in sharp contrast
to the situation with no deception, where the leader's optimal strategy can be
computed in polynomial time, and thus illustrate the intrinsic difficulty of
handling follower deception. Through simulations we also examine the benefit of
considering follower deception in randomly generated games.
