A model of influence in a social network

Grabisch, Michel; Rusinowska, Agnieszka

doi:10.1007/s11238-008-9109-z

Cited by 53 publications

(54 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this paper we continue our work on influence presented in [9,10]. While in the two previous papers on influence we focus on concrete examples, for instance, we define several influence functions and study their properties, the aim of the present paper is to establish exact relations between the key concepts of the influence model and the framework of command games.…”

Section: Introductionmentioning

confidence: 91%

“…in [9][10][11][25][26][27]. We consider a social network with the set of players (agents, voters) denoted by N := {1, ..., n}.…”

Section: The Model Of Influencementioning

confidence: 99%

“…Consider F (S) = ∅, for all S ⊆ N, which is a follower function. We already know from [10,Prop. 7] that an inverse of F by Φ is the reversal function −Id, defined by (−Id)i := −i, for each i ∈ I.…”

Section: If and Only If It Satisfies The Following Three Conditionsmentioning

confidence: 99%

“…Consider F = Id, which is a follower function. We know already from [10,Prop. 6] that an inverse of F is the identity function Id.…”

Section: If and Only If It Satisfies The Following Three Conditionsmentioning

confidence: 99%

“…This influence model is studied e.g. in [10] where, in particular, we introduce weighted influence indices, and consider different influence functions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Influence functions, followers and command games

Grabisch

Rusinowska

2011

Games and Economic Behavior

Self Cite

View full text Add to dashboard Cite

Abstract. We study and compare two frameworks: a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model: influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.JEL Classification: C7, D7

show abstract

Section: Introductionmentioning

confidence: 91%

“…in [9][10][11][25][26][27]. We consider a social network with the set of players (agents, voters) denoted by N := {1, ..., n}.…”

Section: The Model Of Influencementioning

confidence: 99%

Section: If and Only If It Satisfies The Following Three Conditionsmentioning

confidence: 99%

“…Consider F = Id, which is a follower function. We know already from [10,Prop. 6] that an inverse of F is the identity function Id.…”

Section: If and Only If It Satisfies The Following Three Conditionsmentioning

confidence: 99%

“…This influence model is studied e.g. in [10] where, in particular, we introduce weighted influence indices, and consider different influence functions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations