Abstract We introduce the two-step average tree value for transferable utility games with restricted cooperation represented by undirected communication graphs or hypergraphs. The solution can be considered as an alternative both graph and hypergraph games. Instead of averaging players’ marginal contributions corresponding to all admissible rooted spanning trees underlying (hyper)graph, which d...

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with sub-additivity, guarantee the non-emptyness of the core of the game and of all its subgames, namely the game is totally balanced. E...

In this paper, we model energy-limited wireless ad hoc networks as non-transferable-utility cooperative network flow games. We define the %ore capacity region” of a wireless ad hoc network to be the set of Pareto-optimal utility vectors that cannot be blocked by any proper subset of the node set. We show that the core capacity region is non-empty under the linear utility model. Under the many-t...

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person ra...

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average tree solution has been proposed. It was proven that the average tree solution is a core element if the...

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargainin...

We explore the possibility to compare positions in different directed and undirected graphs. assume an agent have a preference relation over weighted (directed undirected) graphs, stating pairwise comparisons between these positions. Ideally, such can be expressed by utility function, where are evaluated their assigned ‘utility’. Extending relations mixture set containing all lotteries graph po...

In a buyer-supplier game, a distinguished player, called the buyer, wishes to purchase some combinatorial object. A set of players, called suppliers, offer pieces of the object for sale. In this paper, we provide a transformation from most combinatorial minimization problems to buyer-supplier games; a characterization of the core of buyer-supplier games in the transferable and non-transferable ...