In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with O(4) constraints whose coefficients belong to {−1, 0, 1}. We discuss the need of having all these constraints and empirically prove that they can be reduced to O(kmax2 ), where kmax is a positive integer comparable with the number of players. A computational experience shows the...

Cooperative games offer an elegant framework to model cooperation among self-interested agents. A central question of these games is how to distribute the payoff to each player when all players cooperate and derive some benefits. In this work, we consider cooperative transferable utility games where a subset of players can form a coalition if and only if they are connected in the underlying com...

Braess' paradox is a classical result in the theory of congestion games. It motivates theoretically why adding resource (e.g., an arc) to network may sometimes worsen, rather than improve, overall performance. Differently from previous literature, which studies non-cooperative game-theoretic setting, this work, framework proposed investigate its occurrence by exploiting cooperative games with t...

Abstract We introduce the concepts of components’ second-order productivities in cooperative games with transferable utility (TU games) a coalition structure (CS and payoffs for one-point solutions CS as generalizations players’ TU (Casajus Discrete Appl Math 304:212–219, 2021). The are conceptualized marginal contributions, that is, how one player affects another player’s contributions to coal...

We study cooperative transferable utility games with a communication structure represented by an undirected graph, i.e., a group of players can cooperate only if they are connected on the graph. This type of games is called graph games and the best-known solution for them is the Myerson value, which is characterized by the component efficiency axiom and the fairness axiom. Recently the average ...

A situation in which a finite set of players can obtain certain payoffs by cooperation be described cooperative game with transferable utility, or simply TU-game. solution for TU-games assigns payoff distributions to every In the literature, various models games restricted found where, instead allowing all subsets player N form, it is assumed that feasible coalitions subset power N. this paper,...

Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation games the kernel is contained in the least core, even if the latter is a lower dimens...

In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation between two adjacent players is established by a directed line segment. Directed path, connecting the initial player with the terminal player, form the coalition ...