Allocation rules for cooperative games with graph and hypergraph communication structure

The thesis is devoted to the study of graph and hypergraph games, which are cooperative games with cooperation restricted by communication structures represented by graphs or hypergraphs. There are four main chapters. Chapter 3 studies a class of graph games, in which several players are selected a priori as main players. A value for graph games with main players is introduced and its characterization is provided in case the underlying communication structure contains no cycles or is a cycle with one main player. Chapters 4 and 5 investigate two generalizations of the average tree solution for graph games to values for hypergraph games and provide several axiomatic characterizations of the new values. Chapter 6 introduces the degree value for hypergraph games. This value highlights the players’ abilities to communicate directly with other players in the communication structure. Characterizations of the value are provided for cycle-free hypergraph games and for arbitrary hypergraph games