  An important aspect of mechanism design in social choice protocols and
multiagent systems is to discourage insincere and manipulative behaviour. We
examine the computational complexity of false-name manipulation in weighted
voting games which are an important class of coalitional voting games. Weighted
voting games have received increased interest in the multiagent community due
to their compact representation and ability to model coalitional formation
scenarios. Bachrach and Elkind in their AAMAS 2008 paper examined divide and
conquer false-name manipulation in weighted voting games from the point of view
of Shapley-Shubik index. We analyse the corresponding case of the Banzhaf index
and check how much the Banzhaf index of a player increases or decreases if it
splits up into sub-players. A pseudo-polynomial algorithm to find the optimal
split is also provided. Bachrach and Elkind also mentioned manipulation via
merging as an open problem. In the paper, we examine the cases where a player
annexes other players or merges with them to increase their Banzhaf index or
Shapley-Shubik index payoff. We characterize the computational complexity of
such manipulations and provide limits to the manipulation. The annexation
non-monotonicity paradox is also discovered in the case of the Banzhaf index.
The results give insight into coalition formation and manipulation.
