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...

The paper concerns a dynamic model of influence in which agents have to make a yes-no decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a...

We study cooperative games associated with a communication structure which takes into account a level of communication between players. Let us consider an undirected communication graph: each node represents a player and there is an edge between two nodes if the corresponding players can...

We generalize a yes-no model of influence in a social network with a single step of mutual influence to a framework with iterated influence. Each agent makes an acceptance- rejection decision and has an inclination to say either ‘yes’ or ‘no’. Due to influence by others, an agent's...

The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition N when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general...

In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of...

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...

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to...

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions...

We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and the concept of semivalues and least square values. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce...