The Not-Preference-Based Hoede-Bakker Index

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

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“…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%

Influence functions, followers and command games

Grabisch

Rusinowska

2011

Games and Economic Behavior

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“…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: 98%

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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“…Such an influence is formally represented by an influence function. The Hoede-Bakker index has been recently studied in [40,41,42,43]. In [42] the authors introduce and investigate a generalization and some modifications of the Hoede-Bakker index in a social network that coincide with some standard power indices, like the Penrose measure (also called the absolute or non-normalized Banzhaf index), the Coleman indices, and the König-Bräuninger index.…”

Section: Introductionmentioning

confidence: 99%

“…[30]). As shown in [40,42], the generalized Hoede-Bakker index measures a kind of 'net Success', i.e., 'SuccessFailure', but if all inclination vectors are equally probable, this index coincides with the measure of 'Decisiveness'.…”

Section: Introductionmentioning

confidence: 99%

Applying relation algebra and RelView to measures in a social network

Berghammer

Rusinowska

Swart

2010

European Journal of Operational Research

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Abstract. We present an application of relation algebra to measure players' 'strength' in a social network with influence between players. In particular, we deal with power, success, and influence of a player as measured by the Hoede-Bakker index, its generalization and modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDDbased tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.

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The Not-Preference-Based Hoede-Bakker Index

Cited by 8 publications

References 14 publications

Influence functions, followers and command games

Influence functions, followers and command games

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

Applying relation algebra and RelView to measures in a social network

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