Different Approaches to Influence Based on Social Networks and Simple Games

Abstract : We present an overview of research on a certain model of influence in a social network. Each agent has to make an acceptance/rejection decision, and he has an inclination to choose either the yes-action or the no-action. The agents are embedded in a social network which models influence between them. Due to the influence, a decision of an agent may differ from his preliminary inclination. Such a transformation between the agents' inclinations and their decisions are represented by an influence function. Follower functions encode the players who constantly follow the opinion of a given unanimous coalition. We examine properties of the influence and follower functions and study the relation between them. The model of influence is also compared to the framework of command games in which a simple game is built for each agent. We study the relation between command games and influence functions. We also define influence indices and determine the relations between these indices and some well-known power indices. Furthermore, we enlarge the set of possible yes/no actions to multi-choice games and investigate the analogous tools related to influence in the multi-choice model.
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Michel Grabisch, Agnieszka Rusinowska. Different Approaches to Influence Based on Social Networks and Simple Games. Adrian van Deemen, Agnieszka Rusinowska. Collective Decision Making: Views from Social Choice and Game Theory, Springer, pp.185-209, 2010, Theory and Decision Library C, Volume 43, ⟨10.1007/978-3-642-02865-6_13⟩. ⟨hal-00514850⟩

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