The Myerson value for augmenting structures

Cooperative games under combinatorial restrictions are cooperative games in which the players have restricted communication possibilities, which are defined by a combinatorial structure. The first model in which the restrictions are defined by the connected subgraphs of a graph is introduced by Myerson [4]. Since then, many other situations where players have communication restrictions have been studied in cooperative game theory. Contributions on graph-restricted games include Owen [5], Borm, Owen, and Tijs [1] and Hamiache [3]. In these models the possibilities of coalition formation are determined by the positions of the players in a communication graph. Another type of combinatorial structure introduced by Gilles, Owen and van den Brink [2] is equivalent to a subclass of antimatroids. This line of research focuses on the possibilities of coalition formation determined by the positions of the players in the so-called permission structure.