An Owen-type value for games with two-level communication structures

We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph, so there is a communication graph between the unions of the coalition structure as well as a communication graph on the players in every union. We also show that, for particular two-level communication structures, the Owen value and the Aumann-Drèze value for games with coalition structures, the Myerson value for communication graph games and the equal surplus division solution appear as special cases of this new value

Two-step values for games with two-level communication structure

TU games with two-level communication structure, in which a two-level communication structure relates fundamentally to the given coalition structure and consists of a communication graph on the collection of the a priori unions in the coalition structure, as well as a collection of communication graphs within each union, are considered. For such games we introduce two families of two-step values inspired by the two-step procedures staying behind the Owen value (Owen, 1977) and the two-step Shapley value (Kamijo, 2009) for games with coalition structures. Our approach is based on the unified treatment of several component efficient values for games with communication structure and it generates two-stage solution concepts that apply component efficient values for games with communication structure on both distribution levels. Comparable axiomatic characterizations are provided

Values for games with two-level communication structures

We consider a new model of a TU game endowed with both coalition and two-level communication structures that applies to various network situations. The approach to the value is close to that of both Myerson (1977) and Aumann and Drèze (1974): it is based on ideas of component efficiency and of one or another deletion link property, and it treats an a priori union as a self-contained unit; moreover, our approach incorporates also the idea of the Owen’s quotient game property (1977). The axiomatically introduced values possess an explicit formula representation and in many cases can be quite simply computed. The results obtained are applied to the problem of sharing an international river, possibly with a delta or multiple sources, among multiple users without international firms

Essays on Cooperative Games with Restricted Cooperation and Simple Games

In this dissertation we propose and characterize new values for cooperative games with restricted cooperation and simple games. In each of the studied models parallel characterizations of different values are proposed to ease the comparison among them

The Average Tree Solution for Multi-choice Forest Games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.

Cooperation and allocation

This thesis deals with various models of cooperation, including games with transferable utility, games with nontransferable utility, bankruptcy situations, communication situations, spillover games and sequencing situations. The focus is on analysing rules for dividing the profits of cooperation. This analysis is performed in terms of properties that one might require of such an allocation mechanism. In addition, properties of the underlying situations and games are studied.

Games with Graph Restricted Communication and Levels Structure of Cooperation

We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new vàlues extending the Shapley value and the Banzhaf value respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in nowadays fully integrated societies