Abstract
Previous works have considered merging in weighted voting games using some well-known power indices, including Shapley-Shubik and Banzhaf indices. Bounds on the amount of power that strategic agents (or manipulators) are likely to gain for the simple case of when there are only two manipulators in the games exist. The bounds on the complicated case of when there are multiple strategic agents, until now, have remained open for the two indices. We use the Shapley-Shubik index and resolve one of these problems by providing two theoretical bounds on merging in weighted voting games with multiple strategic agents.
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