Dominating Set Games

In this paper we study cooperative cost games arising from domination problems on graphs.We introduce three games to model the cost allocation problem and we derive a necessary and su cient condition for the balancedness of all three games.Furthermore we study concavity of these games.game theory;cost allocation;cooperative games

Simple Combinatorial Optimisation Cost Games

In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition.For this class of games, we will characterise core stability and totally balancedness.We continue by characterising exactness and largeness.Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games.Combinatorial optimisation game;core stability;totally balancedness;largeness;exactness

Sequencing Games with Controllable Processing Time

In this paper we study a class of cooperative sequencing games that arise from sequencing situations in which the processing times are not fixed.We show that these games are balanced by obtaining two core elements that depend only on the optimal schedule for the grand coalition.Furthermore we show that, although these games are not convex in general, many marginal vectors are core elements. We also consider convexity for special instances of the sequencing situation.cooperative games

On the Balancedness of Relaxed Sequencing Games

This paper shows that some classes of relaxed sequencing games, which arise from the class of sequencing games as introduced in Curiel, Pederzoli, Tijs (1989), are balanced.sequencing situations;sequencing games;balancedness;game theory

Sequencing Games with Controllable Processing Time

In this paper we study a class of cooperative sequencing games that arise from sequencing situations in which the processing times are not fixed.We show that these games are balanced by obtaining two core elements that depend only on the optimal schedule for the grand coalition.Furthermore we show that, although these games are not convex in general, many marginal vectors are core elements. We also consider convexity for special instances of the sequencing situation.

Cooperation in Networks and Scheduling

This thesis deals with various models of cooperation in networks and scheduling. The main focus is how the benefits of this cooperation should be divided among the participating individuals. A major part of this analysis is concerned with stability of the cooperation. In addition, allocation rules are investigated, as well as properties of the underlying situations and games.

Convexity and Marginal Vectors

In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that the relative number of marginals needed to characterize convexity converges to zero.game theory;convexity;marginal vectors

Characterizing Convexity of Games using Marginal Vectors

In this paper we study the relation between convexity of TU games and marginal vectors.We show that if specfic marginal vectors are core elements, then the game is convex.We characterize sets of marginal vectors satisfying this property, and we derive the formula for the minimum number of marginal vectors in such sets.game theory;convexity;marginal vectors

Simple Combinatorial Optimisation Cost Games

In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition.For this class of games, we will characterise core stability and totally balancedness.We continue by characterising exactness and largeness.Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games.

Core Stability in Chain-Component Additive Games

Chain-component additive games are graph-restricted superadditive games, where an exogenously given line-graph determines the cooperative possibilities of the players.These games can model various multi-agent decision situations, such as strictly hierarchical organisations or sequencing / scheduling related problems, where an order of the agents is fixed by some external factor, and with respect to this order only consecutive coalitions can generate added value. In this paper we characterise core stability of chain-component additive games in terms of polynomial many linear inequalities and equalities that arise from the combinatorial structure of the game.Furthermore we show that core stability is equivalent to essential extendibility.We also obtain that largeness of the core as well as extendibility and exactness of the game are equivalent properties which are all sufficient for core stability.Moreover, we also characterise these properties in terms of linear inequalities.Core stability;graph-restricted games;large core;exact game