False‐Name Manipulation in Weighted Voting Games: Empirical and Theoretical Analysis

Abstract

Weighted voting games are important in multiagent systems because of their usage in automated decision making. However, they are not immune from the vulnerability of false-name manipulation by strategic agents that may be present in the games. False-name manipulation involves an agent splitting its weight among several false identities in anticipation of power increase. Previous works have considered false-name manipulation using the well-known Shapley-Shubik and Banzhaf power indices. Bounds on the extent of power that a manipulator may gain exist when it splits into k D 2 false identities for both the Shapley-Shubik and Banzhaf indices. The bounds when an agent splits into k > 2 false identities, until now, have remained open for the two indices. This article answers this open problem by providing four nontrivial bounds when an agent splits into k > 2 false identities for the two indices. Furthermore, we propose a new bound on the extent of power that a manipulator may gain when it splits into several false identities in a class of games referred to as excess unanimity weighted voting games. Finally, we complement our theoretical results with empirical evaluation. Results from our experiments confirm the existence of beneficial splits into several false identities for the two indices, and also establish that splitting into more than two false identities is qualitatively different than the previously known splitting into exactly two false identities.

Manipulation-resistant false-name-proof facility location mechanisms for complex graphs

“…Conitzer [15] analyzed false-name-proof mechanisms in voting scenarios; Moulin [45] studied a related problem of routing-proofness in networks; Penna et al [52] studied cost-sharing games; Todo et al [68] studied mechanisms for online auction mechanisms, in which bidders arrive and depart over time; Todo and Conitzer [65] studied matching mechanisms; and Tsuruta et al [71] studied false-name-proof cake-cutting procedures. A similar concept was also applied for cooperative games by Aziz et al [4] and Lasisi and Allan [37]. In these works, they analyzed, given a weighted voting scenario, by how much an agent can change her power (as measured by the Shapley-Shubik index or the Banzhaf index), by splitting her weight among several false-name identities.…”

Worst-case Bounds on Power vs. Proportion in Weighted Voting Games with an Application to False-name Manipulation

“…• General splits -We consider splits into multiple identities, rather than splits into two or three identities. Lasisi and Allan (2017) initiated work on this more general problem, where they show some upper and lower bounds for the individual power gain from general splits compared to the original power. These bounds assume that only a single agent splits, whereas the bounds we provide hold under any combination of strategic manipulations by the agents.…”