  We study an online learning problem in general-sum Stackelberg games, where
players act in a decentralized and strategic manner. We study two settings
depending on the type of information for the follower: (1) the limited
information setting where the follower only observes its own reward, and (2)
the side information setting where the follower has extra side information
about the leader's reward. We show that for the follower, myopically best
responding to the leader's action is the best strategy for the limited
information setting, but not necessarily so for the side information setting --
the follower can manipulate the leader's reward signals with strategic actions,
and hence induce the leader's strategy to converge to an equilibrium that is
better off for itself. Based on these insights, we study decentralized online
learning for both players in the two settings. Our main contribution is to
derive last-iterate convergence and sample complexity results in both settings.
Notably, we design a new manipulation strategy for the follower in the latter
setting, and show that it has an intrinsic advantage against the best response
strategy. Our theories are also supported by empirical results.
