Showing papers by "Ruud Hendrickx published in 2002"

A note on NTU convexity

Abstract: For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation. For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games that generalise the marginalistic interpretation of convexity.

A note on NTU-convexity

Abstract: For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation. For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games that generalise the marginalistic interpretation of convexity.

The constrained equal award rule for bankruptcy problems with a priori unions

Abstract: We consider bankruptcy problems where the creditors are grouped in a structure of a priori unions. Our main objective is to define a rule for dividing the available estate among all the creditors, which takes the structure of unions into account. In a first step we introduce disjoint issue allocation situations. These are a special case of multi-issue allocation situations as introduced in Calleja, Borm and Hendrickx (2001); those in which every player is involved in exactly one issue. Every bankruptcy situation with a priori unions gives rise to a disjoint issue allocation situation, where the issues correspond to the unions. This allows us to define a class of cooperative games with transferable utility in order to analyse bankruptcy problems with a priori unions. These games turn out to be exact. We provide different ways to extend a rule on the class of the standard bankruptcy problems to the class of bankruptcy problems with a priori unions. We concentrate in a rule that is an extension of the constrained equal award rule for standard bankruptcy problems. We study properties and provide two axiomatic characterizations of this rule. We also see that for a bankruptcy problem with a priori unions, this rule coincides with a certain cooperative solution concept for games corresponding to bankruptcy problems with unions. We also define consistency properties for this kind of problems, based on O�Neill (1982). Finally, we give some applications.

Drop Out Monotonic Rules for Sequencing Situations

Abstract: This note introduces a new monotonicity property for sequencing situations. A sequencing rule is called drop out monotonic if no player will be worse off whenever one of the players decides to drop out of the queue before processing starts. This intuitively appealing property turns out to be very strong: we show that there is at most one rule satisfying both stability and drop out monotonicity. For the standard model of linear cost functions, the existence of this rule is established. Copyright Springer-Verlag 2005(This abstract was borrowed from another version of this item.)

A Relation between Nash Equilibria and Correlated Equilibria

Abstract: In this paper we investigate the set of correlated equilibria of bimatrix games. These equilibria are interesting, because they can result in outcome profiles that are not feasible as a result of Nash equilibria. After giving an example to illustrate the various concepts, we present a Projection Theorem which relates the two types of equilibria. Some lemmas are provided to clarify and extend this theorem.

Spillovers and Strategic Cooperative Behaviour

Abstract: In this paper, we analyse cooperative situations in which the formation of a coalition results in spillovers to the players outside that coalition. To this type of situation a new type of game, a spillover game, is associated, in which both cooperative and strategic elements play a role. Some basic game theoretical concepts are analysed for this new class of games and illustrated by means of three applications of our model: government situations, public-private connection problems and cartels in oligopolistic markets.

The Constrained Equal Award Rule for Bankruptcy Problems with a Priori Unions

Abstract: In this paper, we provide four extensions of the constrained equal award rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The four new extensions are illustrated by a specific application.