Influence functions, followers and command games

Grabisch, Michel; Rusinowska, Agnieszka

doi:10.1016/j.geb.2010.06.003

Cited by 24 publications

(23 citation statements)

References 32 publications

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“…In Grabisch and Rusinowska (2009), we show that the framework of influence is more general than a cooperative model of command games presented in Hu and Shapley (2003a,b). This line of research is continued in Grabisch and Rusinowska (2011a), where the exact relations between the key concepts of the influence model and the framework of command games are established.…”

Section: The Present Papermentioning

confidence: 99%

A model of influence based on aggregation functions

Grabisch

Rusinowska

2013

Mathematical Social Sciences

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The paper concerns a dynamic model of influence in which agents have to make a yes-no decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a Markov chain. In the paper, we investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents, possibly including himself. We provide a general analysis of convergence in the aggregation model and give more practical conditions based on influential players. We show that the process of influence converges always to one of the two consensus states, and there may exist other terminal classes, which are either cyclic or union of Boolean lattices. We give sufficient conditions for avoiding these additional terminal classes, based on properties of the graph of influence and influential players. We also introduce the notion of influential coalition and show that it can fully describe terminal classes. Some important families of aggregation functions are discussed. JEL Classification: C7, D7Keywords: influence, aggregation function, convergence, terminal class, influential coalition, social network Corresponding author: Michel Grabisch * We like to thank Philippe Solal and Eric Rémila for pointing out an error in a previous version of Theorem 2. This research project is supported by the

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Section: The Present Papermentioning

confidence: 99%

A model of influence based on aggregation functions

Grabisch

Rusinowska

2013

Mathematical Social Sciences

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“…For some influence functions we define the equivalent command games. -In [30] we establish the exact relations between the key concepts of the influence model and the framework of command games. We deliver sufficient and necessary conditions for a function to be a follower function, and describe the structure of the set of all influence functions that lead to a given follower function.…”

Section: Further Research On Influencementioning

confidence: 99%

Social Networks: Prestige, Centrality, and Influence

Rusinowska

Berghammer

Swart

et al. 2011

Lecture Notes in Computer Science

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Abstract. We deliver a short overview of different centrality measures and influence concepts in social networks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-related measures. We consider centrality of a node and of a network. Moreover, we give a classification of the centrality measures based on a topology of network flows. Furthermore, we present a certain model of influence in a social network and discuss some applications of relation algebra and RelView to this model.

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“…The point is that, theoretically, there are certain observations of coalitions' initial inclinations and followers' behaviors capable of ruling out the possibility that the final decisions are the result of an influence process of the form captured by their model. Grabisch and Rusinowska (2011) [30] tells us precisely what those observations are. The paper provides necessary and sufficient conditions for any given function mapping subsets of N to subsets of N to be the follower function of some influence function.…”

Section: Introductionmentioning

confidence: 95%

“…The first one is called the model of influence and is based on a framework first introduced by Hoede and Bakker (1982) [25] in order to measure the decisional power of agents in a social network and, subsequently, extended by Grabisch and Rusinowska (2010b) [26] to study influence. (This framework has been studied in-depth by Rusinowska and De Swart (2007) [27], Grabisch and Rusinowska (2009) [28], (2010a) [29], (2010b) [26], (2011) [30] and Rusinowska (2008) [31]. For a survey of the work, see Grabisch and Rusinowska (2010c) [32].)…”

Section: Introductionmentioning

confidence: 99%

“…The paper provides necessary and sufficient conditions for any given function mapping subsets of N to subsets of N to be the follower function of some influence function. The Hu and Shapley (2003a) [33] (2003b) [34] command games framework is closely related to the Grabisch and Rusinowska model of influence (Grabisch and Rusinowska (2011) [30] studies the relation between them). Given a set, N , of agents and two possible actions, the central element in the command games literature is a simple game for each agent i describing the coalitions that lead the agent to take the high action i.…”

Section: Introductionmentioning

confidence: 99%

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From Observable Behaviors to Structures of Interaction in Binary Games of Strategic Complements

Barraquer

2013

Entropy

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Consider a setting in which agents can take one of two ordered actions and in which the incentive to take the high action increases in the number of other agents taking it. Furthermore, assume that we do not know anything else about the game being played. What can we say about the details of the interaction between actions and incentives when we observe a set or a subset of all possible equilibria? In this paper, we study this question by exploring three nested classes of games: (a) binary games of strategic complements; (b) games in (a) that admit a network representation; and (c) games in (b) in which the network is complete. Our main results are the following: It has long been established in the literature that the set of pure strategy Nash equilibria of any binary game of strategic complements among a set, N , of agents can be seen as a lattice on the set of all subsets of N under the partial order defined by the set inclusion relation (⊆). If the game happens to be strict in the sense that agents are never indifferent among outcomes (games in (a)), then the resulting lattice of equilibria satisfies a straightforward sparseness condition. (1) We show that, in fact, for each such lattice, L, there is a game in (a), such that its set of equilibria is L (we say that such a game expresses L); (2) We show that there exists a game in (b), whose set of equilibria contains a given collection, C, of subsets of N , if and only C satisfies the sparseness condition, and the smallest game in (a) expressing C is trade robust; (3) We show that there exists a game on the complete graph (games in (c)), whose set of equilibria coincides with some collection, C, if and only if C is a chain satisfying the sparseness condition.

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Influence functions, followers and command games

Cited by 24 publications

References 32 publications

A model of influence based on aggregation functions

A model of influence based on aggregation functions

Social Networks: Prestige, Centrality, and Influence

From Observable Behaviors to Structures of Interaction in Binary Games of Strategic Complements

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