On Hierarchies and Communication

Many economic organizations have some relational structure, meaning that economic agents do not only differ with respect to certain individual characteristics such as wealth and preferences, but also belong to some relational structure in which they usually take different positions. Two examples of such structures are communication networks and hierarchies. In the literature the distinction between these two types of relational structures is not always clear. In models of restricted cooperation this distinction should be defined by properties of the set of feasible coalitions. We characterize the feasible sets in communication networks and compare them with feasible sets arising from hierarchies

The Minimal Dominant Set is a Non-Empty Core-Extension

A set of outcomes for a TU-game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core.Core, Non-emptiness, Indirect dominance, Outsider-independence

The core of games on ordered structures and graphs

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results

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An optimal bound to access the core in TU-games

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2

An optimal bound to access the core in TU-games

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2

Partition-based Stability of Coalitional Games

We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings. This principle of consensual blocking, as well as the traditional core-defining principle of unilateral blocking and one straddling in between, can all be applied to partition-allocation pairs. Each such pair is made up of a partition of the grand coalition and a corresponding allocation vector whose components are individually rational and efficient for the various constituent coalitions of the given partition. For the resulting strong, medium, and weak stability concepts, the first is core-compatible in that the traditional core exactly contains those allocations that are associated through this strong stability concept with the all-consolidated partition consisting of only the grand coalition. Probably more importantly, the latter medium and weak stability concepts are universal. By this, we mean that any game, no matter how ``poor'' it is, has its fair share of stable solutions. There is also a steepest ascent method to guide the convergence process to a mediumly stable partition-allocation pair from any starting partition