We consider the travelling salesperson game (TSG) in which agents correspond to a set of locations, and the cost of each subset of locations is the length of the optimal tour for that subset. The Shapley value, one of the most important normative division schemes in cooperative games, is a principled way of dividing transport costs among such locations. We prove that approximating the Shapley v...

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 ...

The paper characterizes the position value and the Myerson value for communication situations. The position value is originally defined as the sum of half the Shapley value of the link games but is also represented by the Shapley value of a modification of the link games. That modification is called the divided link games. In addition, by constructing coalition structures of the divided links f...

We study the asymptotic properties of the Shapley value of patent licensing games with the Cournot competition, shedding light on its relations to the nucleolus, core and bargaining set. The Shapley value of the outside patentee of a non-drastic cost-reducing innovation converges to 2(a − c), which coincides with the patentee’s profit through non-cooperative licensing by means of upfront fee (o...

The main aim of this article is to compare the results of classical Shapley value concept with results of the Shapley value extended to the cooperative games with fuzzy coalitions applied on the real data of the cooperative simple game – in this case the data from the voting in the Lower House of the Czech Parliament 20022012. One of the most intriguing tasks is to describe real system problems...

In this paper we survey author’s recent results on quantitative extensions of Ramsey theory. In particular, we discuss our recent results on Folkman numbers, induced bipartite Ramsey graphs, and explicit constructions of Ramsey graphs.

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it an O...

The Shapley value and Banzhaf index are two well known indices for measuring the power a player has in a voting game. However, the problem of computing these indices is computationally hard. To overcome this problem, we analyze approximation methods for computing these indices. Although these methods have polynomial time complexity, finding an approximate Shapley value using them is easier than...