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A model of influence with a continuum of actions
, 2011
"... We generalize a twoaction (yesno) model of influence to a framework in which every player has a continuum of actions, among which he has to choose one. We assume the set of actions to be an interval. Each player has an inclination to choose one of the actions. Due to influence among players, the f ..."
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We generalize a twoaction (yesno) model of influence to a framework in which every player has a continuum of actions, among which he has to choose one. We assume the set of actions to be an interval. Each player has an inclination to choose one of the actions. Due to influence among players, the final decision of a player, i.e., his choice of one action, may be different from his original inclination. In particular, a coalition of players with the same inclination may influence another player with different inclination, and as a result of this influence, the decision of the player is closer to the inclination of the influencing coalition than his inclination was. We introduce a measure of such a positive influence of a coalition on a player. Several unanimous influence functions in this generalized framework are considered. Also the set of fixed points under a given influence function is analyzed. Furthermore, we study linear influence functions and discuss their convergence. For a linear unanimous function, we find necessary and sufficient conditions for the existence of the positive influence of a coalition on a player, and we calculate the value of the influence index. We also introduce a measure of a negative influence of a coalition on a player.
Power Measures and Solutions for Games
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1 Gerard van der Laan 2
, 2001
"... Many economic and social situations can be represented by a digraph. Both axiomatic and iterative methods to determine the strength or power of all the nodes in a digraph have been proposed in the literature. We propose a new method, where the power of a node is determined by both the number of its ..."
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Many economic and social situations can be represented by a digraph. Both axiomatic and iterative methods to determine the strength or power of all the nodes in a digraph have been proposed in the literature. We propose a new method, where the power of a node is determined by both the number of its successors, as in axiomatic methods, and the powers of its successors, as in iterative methods. Contrary to other iterative methods, we obtain a full ranking of the nodes for any digraph. The new power function, called the positional power function, can either be determined as the unique solution to a system of equations, or as the limit point of an iterative process. The solution is also explicitly characterized. This characterization enables us to derive a number of interesting properties of the positional power function. Next we consider a number of extensions, like the positional weakness function and the position function. JEL classication: C60, C70, D70 Key words: graph, tournament, power function
A Service of zbw Power Measures and Solutions for Games under Precedence Constraints Power Measures and Solutions for Games under Precedence Constraints
"... StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, ..."
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StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter OpenContentLizenzen (insbesondere CCLizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Abstract In the literature, there exist several models where a cooperative TUgame is enriched with a hierarchical structure on the player set that is represented by a directed graph or digraph. In this paper we consider the games under precedence constraints introduced by
Anonymous social influence
, 2013
"... We study a stochastic model of influence where agents have “yes ” or “no ” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ..."
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We study a stochastic model of influence where agents have “yes ” or “no ” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extend. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most ” or “at least a few”.
Anonymous Social Influence†
, 2013
"... We study a stochastic model of influence where agents have “yes” or “no ” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ..."
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We study a stochastic model of influence where agents have “yes” or “no ” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extend. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most ” or “at least a few”.
Ordered Weighted Averaging in Social Networks
, 2012
"... We study a stochastic model of influence where agents have yesno inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered ..."
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We study a stochastic model of influence where agents have yesno inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators. This allows to study situations where the influence process resembles a majority vote, which are not covered by the classical approach of weighted averaging aggregation. We provide an analysis of the speed of convergence and the probabilities of absorption by different terminal classes. We find a necessary and sufficient condition for convergence to consensus and characterize terminal states. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extend. Furthermore, we apply our results to fuzzy linguistic quantifiers.