  Prior work on the complexity of bribery assumes that the bribery happens
simultaneously, and that the briber has full knowledge of all voters' votes.
But neither of those assumptions always holds. In many real-world settings,
votes come in sequentially, and the briber may have a use-it-or-lose-it moment
to decide whether to bribe/alter a given vote, and at the time of making that
decision, the briber may not know what votes remaining voters are planning on
casting.
  In this paper, we introduce a model for, and initiate the study of, bribery
in such an online, sequential setting. We show that even for election systems
whose winner-determination problem is polynomial-time computable, an online,
sequential setting may vastly increase the complexity of bribery, in fact
jumping the problem up to completeness for high levels of the polynomial
hierarchy or even PSPACE. On the other hand, we show that for some natural,
important election systems, such a dramatic complexity increase does not occur,
and we pinpoint the complexity of their bribery problems in the online,
sequential setting.
