Divide and conquer: false-name manipulations in weighted voting games

In this paper, we study false-name manipulations in weighted voting games. Weighted voting is a well-known model of cooperation among agents in decision-making domains. In such games, each of the players has a weight, and a coalition of players wins the game if its total weight exceeds a certain quota. While a player's ability to influence the outcome of the game is related to its weight, it is not always directly proportional to it. This observation has led to the concept of a power index, which is a measure of an agent's "real power" in this domain. One prominent power index is the Shapley--Shubik index, which has been widely used to analyze political power. This index is equal to the Shapley value of the player in the game. If an agent can alter the game so that his Shapley--Shubik index increases, this will mean that he has gained power in the game. Moreover, the Shapley value is often used to distribute the gains of the grand coalition. In this case, this alteration will also increase the agent's payoffs. One way in which an agent can change the game (and hence his payoffs) is by distributing his weight among several false identities. We call this behavior a false-name manipulation. We show that such manipulations can indeed increase an agent's power, as determined by the Shapley-Shubik power index, or his payoffs, as given by the Shapley value. We provide upper and lower bounds on the effects of such manipulations. We then study this issue from the computational perspective, and show that checking whether a beneficial split exists is NP-hard. We also discuss efficient algorithms for restricted cases of this problem, as well as randomized algorithms for the general case.