Stef Tijs

On the position value for communication situations

A new solution concept for communication situations is considered: the position value. This concept is based on an evaluation of the importance of the various communication links between the players. An axiomatic characterization of the position value is provided for the class of communication situations where the communication graphs contain no cycles. Furthermore, relations with the Myerson value are discussed,and, for special classes of communication situations, elegant calculation methods for their position values are described.

Cores and related solution concepts for multi-choice games

A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. Cooperative games form a subclass of the class of multi-choice games.This paper extends some solution concepts for cooperative games to multi-choice games. In particular, the notions of core, dominance core and Weber set are extended. Relations between cores and dominance cores and between cores and Weber sets are extensively studied. A class of flow games is introduced and relations with non-negative games with non-empty cores are investigated.

On Cores and Stable Sets for Fuzzy Games

In this paper, cores and stable sets for games with fuzzy coalitions are introduced and their relations studied. For convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set. Also relations between cores and stable sets of fuzzy clan games are discussed.

CONGESTION GAMES AND POTENTIALS RECONSIDERED

In congestion games, players use facilities from a common pool. The benefit that a player derives from using a facility depends, possibly among other things, on the number of users of this facility. The paper gives an easy alternative proof of the isomorphism between exact potential games and the set of congestion games introduced by Rosenthal (1973). It clarifies the relations between existing models on congestion games, and studies a class of congestion games where the sets of Nash equilibria, strong Nash equilibria and potential-maximizing strategies coincide. Particular emphasis is on the computation of potential-maximizing strategies.

Cooperation under Interval Uncertainty

In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions are introduced and characterizations are given.

Sequencing and Cooperation

In machine scheduling the first problem is to find a timetable that is optimal with respect to some efficiency criterion. If the jobs come from different clients the solution of the optimization problem is not the end of the story. In addition, we have to decide how the minimal total cost must be distributed among the parties involved. In this note, cost allocation problems will be considered to arise from one-machine scheduling problems with an additive and weakly increasing cost function. We will show that the cooperative games related to these cost allocation problems have a nonempty core. Furthermore, we give a rule that assigns a core element of the associated cost saving game to each scheduling problem of this kind and an initial order of the jobs.

Minimum cost spanning tree games and population monotonic allocation schemes

In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme.As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0-1 cost functions.It turns out that the Subtraction Algorithm is closely related to the famous algorithm of Kruskal for the determination of minimum cost spanning trees.For variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

On games corresponding to sequencing situations with ready times

This paper considers the special class of cooperative sequencing games that arise from one-machine sequencing situations in which all jobs have equal processing times and the ready time of each job is a multiple of the processing time.By establishing relations between optimal orders of subcoalitions, it is shown that each sequencing game within this class is convex.

The general nucleolus and the reduced game property

The nucleolus of a TU game is a solution concept whose main attraction is that it always resides in any nonempty ɛ-core. In this paper we generalize the nucleolus to an arbitrary pair (Π,F), where Π is a topological space andF is a finite set of real continuous functions whose domain is Π. For such pairs we also introduce the “least core” concept. We then characterize the nucleolus forclasses of such pairs by means of a set of axioms, one of which requires that it resides in the least core. It turns out that different classes require different axiomatic characterizations.One of the classes consists of TU-games in which several coalitions may be nonpermissible and, moreover, the space of imputations is required to be a certain “generalized” core. We call these gamestruncated games. For the class of truncated games, one of the axioms is a new kind ofreduced game property, in which consistency is achieved even if some coalitions leave the game, being promised the nucleolus payoffs. Finally, we extend Kohlbergs characterization of the nucleolus to the class of truncated games.

Permutation games: Another class of totally balanced games

SummaryA class of cooperative games in characteristic function form arising from certain sequencing problems and assignment problems, is introduced. It is shown that games of this class are totally balanced. In the proof of this fact we use the Birkhoff-von Neumann theorem on doubly stochastic matrices and the Bondareva-Shapley theorem on balanced games. It turns out that this class of permutation games coincides with the class of totally balanced games if the number of players is smaller than four. For larger games the class of permutation games is a nonconvex subset of the convex cone of totally balanced games.ZusammenfassungWir führen eine Klasse von kooperativen Spielen in charakteristischer Funktionsform ein, die bei gewissen Folgeproblemen und Zuordnungsproblemen auftreten. Wir zeigen, daß diese Spiele vollständig balanciert sind. Zum Beweis verwenden wir den Satz von Birkhoff-von Neumann über doppelt stochastische Matrizen und den Satz von Bondareva-Shaplex über balancierte Spiele. Es zeigt sich, daß diese Klasse von Permutationsspielen mit der Klasse von vollständig balancierten Spiele übereinstimmt, falls die Zahl der Spieler kleiner als vier ist. Für größere Spiele ist die Klasse der Permutationsspiele eine nichtkonvexe Teilmenge des konvexen Kegels der vollständig balancierten Spiele.