Decomposition of Network Communication Games

Using network control structures this paper introduces network communication games as a generalization of vertex games and edge games corresponding to communication situations and studies their decomposition into unanimity games. We obtain a relation between the dividends of the network communication game and the underlying transferable utility game, which depends on the structure of the undirected graph. This relation extends the computational results for tree communication networks to general undirected graphs and is used to derive new characterizations of the Myerson value and the position value. Moreover, network communication games also allow to consider both the vertices and the edges of the graph as players, leading to a new network value

Matching structure and bargaining outcomes in buyer–seller networks

We examine the relationship between the matching structure of a bipartite (buyer-seller) network and the (expected) shares of the unit surplus that each connected pair in this network can create. We show that in different bargaining environments, these shares are closely related to the Gallai-Edmonds Structure Theorem. This theorem characterizes the structure of maximum matchings in an undirected graph. We show that the relationship between the (expected) shares and the tructure Theorem is not an artefact of a particular bargaining mechanism or trade centralization. However, this relationship does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values