Social Influence as a Voting System: a Complexity Analysis of Parameters and Properties

TL;DR

This paper models social influence as a voting system using influence games, analyzing their expressiveness, computational complexity, and properties under the linear threshold influence model.

Contribution

It introduces influence games as a framework capturing simple games and provides complexity analyses for various measures and properties within this model.

Findings

Influence games can represent all simple games.

Computational complexity results for influence measures and properties.

Tighter complexity bounds in extremal influence propagation cases.

Abstract

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.