In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performan...

We provide a new characterization of the Shapley value neither using the e¢ciency axiom nor the additivity axiom. In this characterization, e¢ciency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615–621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are ...

Coalitional games allow subsets (coalitions) of players to cooperate to receive a collective payoff. This payoff is then distributed “fairly” among the members of that coalition according to some division scheme. Various solution concepts have been proposed as reasonable schemes for generating fair allocations. The Shapley value is one classic solution concept: player i’s share is precisely equ...

A game on a convex geometry is a real-valued function de0ned on the family L of the closed sets of a closure operator which satis0es the 0nite Minkowski–Krein–Milman property. If L is the boolean algebra 2 then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axiom...

The Shapley value solution occupies a central place in fair division literature, specially in settings where a set of positions in a queue need to be shared between a set of agents using payments. But computing the Shapley value of an agent requires solving exponential number of optimization problems (marginal value problem). Moreover, it requires exact knowledge of valuation functions of agent...

We characterize the Extended, Generalized Shapley Value of McQuillin [6] using an ‘efficiency’ condition and two ‘balance’ conditions. One feature of this charaterization is that the conditions only have to apply for a single game.

Within the current Internet, autonomous ISPs implement bilateral agreements, with each ISP establishing agreements that suit its own local objective to maximize its profit. Peering agreements based on local views and bilateral settlements, while expedient, encourage selfish routing strategies and discriminatory interconnections. From a more global perspective, such settlements reduce aggregate ...

We design a simple non-cooperative mechanism in the classs of NTUgames. We study it in the context of a particular class of pure exchange economies. When the corresponding NTU game (N, V ) satisfies that V (N) is flat, the only payoff which arises in equilibrium is the Shapley NTU value.