  We study a two-player Stackelberg game with incomplete information such that
the follower's strategy belongs to a known family of parameterized functions
with an unknown parameter vector. We design an adaptive learning approach to
simultaneously estimate the unknown parameter and minimize the leader's cost,
based on adaptive control techniques and hysteresis switching. Our approach
guarantees that the leader's cost predicted using the parameter estimate
becomes indistinguishable from its actual cost in finite time, up to a
preselected, arbitrarily small error threshold. Also, the first-order necessary
condition for optimality holds asymptotically for the predicted cost.
Additionally, if a persistent excitation condition holds, then the parameter
estimation error becomes bounded by a preselected, arbitrarily small threshold
in finite time as well. For the case where there is a mismatch between the
follower's strategy and the parameterized function that is known to the leader,
our approach is able to guarantee the same convergence results for error
thresholds larger than the size of the mismatch. The algorithms and the
convergence results are illustrated via a simulation example in the domain of
network security.
