  The Byzantine distributed quickest change detection (BDQCD) is studied, where
a fusion center monitors the occurrence of an abrupt event through a bunch of
distributed sensors that may be compromised. We first consider the binary
hypothesis case where there is only one post-change hypothesis and prove a
novel converse to the first-order asymptotic detection delay in the large mean
time to a false alarm regime. This converse is tight in that it coincides with
the currently best achievability shown by Fellouris et al.; hence, the optimal
asymptotic performance of binary BDQCD is characterized. An important
implication of this result is that, even with compromised sensors, a 1-bit link
between each sensor and the fusion center suffices to achieve asymptotic
optimality. To accommodate multiple post-change hypotheses, we then formulate
the multi-hypothesis BDQCD problem and again investigate the optimal
first-order performance under different bandwidth constraints. A converse is
first obtained by extending our converse from binary to multi-hypothesis BDQCD.
Two families of stopping rules, namely the simultaneous $d$-th alarm and the
multi-shot $d$-th alarm, are then proposed. Under sufficient link bandwidth,
the simultaneous $d$-th alarm, with $d$ being set to the number of honest
sensors, can achieve the asymptotic performance that coincides with the derived
converse bound; hence, the asymptotically optimal performance of
multi-hypothesis BDQCD is again characterized. Moreover, although being shown
to be asymptotically optimal only for some special cases, the multi-shot $d$-th
alarm is much more bandwidth-efficient and energy-efficient than the
simultaneous $d$-th alarm. Built upon the above success in characterizing the
asymptotic optimality of the BDQCD, a corresponding leader-follower Stackelberg
game is formulated and its solution is found.
