We generalize a two-action (yes-no) 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,...

An element of the possibly unbounded core of a cooperative game with precedence constraints belongs to its bounded core if any transfer to a player from any of her subordinates results in payoffs outside the core. The bounded core is the union of all bounded faces of the core, it is nonempty if...

We deliver a short overview of di erent 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,...

Cooperation structures without any {\it a priori} assumptions on the combinatorial structure of feasible coalitions are studied and a general theory for mar\-ginal values, cores and convexity is established. The theory is based on the notion of a Monge extension of a general characteristic...

Bi-capacities are a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours. After a short presentation of the basis structure, we introduce the Shapley value and...

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of...

An extension to the classical notion of core is the notion of $k$-additive core, that is, the set of $k$-additive games which dominate a given game, where a $k$-additive game has its Möbius transform (or Harsanyi dividends) vanishing for subsets of more than $k$ elements. Therefore, the...