Cooperative games on antimatroids are cooperative games in which coalition formation is restricted by a combinatorial structure which generalizes permission structures. These games group several well-known families of games which have important applications in economics and politics. The current paper establishes axioms that determine the restricted Banzhaf value for cooperative games on antima...

We show that for every cooperative game a corresponding set game can be defined, called the standard set game. Values for set games can be applied to this standard game and determine allocations for the cooperative game. On the other hand, notions for cooperative games, like the Shapley value, the τ−value or the core can be considered in the context of the standard set games.

In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space. Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic cooperative gam...

We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibr...

A generalized model of games is proposed, with which both cooperative games and non-cooperative games can be expressed and analyzed, as well as those games that are neither cooperative nor non-cooperative. The model is based on relationships between players and supposed relationships. A relationship is a numerical value that denotes how one player cares for the payoffs of another player. A supp...

Cooperative boolean games are coalitional games with both goals and costs associated to actions, and dependence networks for boolean games are a kind of social networks representing how the actions of other agents have an influence on the achievement of an agent’s goal. In this paper, we introduce two new types of dependence networks, called the abstract dependence network and the refined depen...

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. We investigate a class of cooperative games that generalizes some economic applications with a similar structure. These are the so-called line-graph games being cooperative TU-games in which the players are linearly ordered. Examples of situations that can be modeled like this are sequencin...

Results of game theory are often the keys to decisions of economical and political executives. They are also used to create internal tools of many decision making software. For example, coordination games may be cooperative games, when the players choose the strategies by a consensus decision making process, and game trees are used to represent some key cooperative games. Our theory of cooperat...

In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values Weber (1988) and quasi-probabilistic Bilbao et al. (2001). Applications to Multi-Touch Attribution interpretability Machine-Learning prediction models motivate these new developments (Lundberg Lee, 2017; Ribeiro al., 2016; Strumbelj Kononenko, 2013; Shrikumar Datta Bach 2015). We de...