A theory of decisional power

Games and Economic Behavior

2011

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

“…The framework of influence that we study in this paper has been originally introduced in [12], and next analyzed e.g. in [9][10][11][25][26][27].…”

Section: The Model Of Influencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence functions, followers and command games

Grabisch

Games and Economic Behavior

2011

“…When clear from the context, we will skip '(B, gd)' in the expressions above; so, for instance, we may write I +− k instead of I +− k (B, gd). In order to measure the strength of the players in a voting situation of a social network, where the inclination of a player may be different from its final decision due to influences from other players, the subsequent definition has been introduced in [25] (note, that n is the number of players): Definition 2.1.1 Given B ∈ B and gd ∈ G, the decisional power (the Hoede-Bakker index) of a player k ∈ P is defined as follows:…”

Section: The Hoede-bakker Index and Its Modificationsmentioning

confidence: 99%

Applying relation algebra and RelView to measures in a social network

Berghammer

European Journal of Operational Research

Swart

2010

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.

“…Then, a group decision gd(Bi) is made. This is in fact the framework considered originally in Hoede and Bakker (1982), who proposed the concept of decisional power of a player (the Hoede-Bakker index), and which was later generalized and modified in Rusinowska and De Swart (2006).…”

Section: Introductionmentioning

confidence: 99%

A model of influence in a social network

Grabisch

2008

Theory Decis

Abstract. In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index -the notion which computes the overall decisional 'power' of a player in a social network. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power.JEL Classification: C7, D7