Coalitional Manipulation on Communication Network

In an abstract model of division problems, we study division rules that are not manipulable through a reallocation of individual characteristic vectors within a coalition (e.g. reallocation of claims in bankruptcy problems). A coalition can be formed if members of the coalition are connected on a communication network, or a graph. We offer a characterization of non-manipulable division rules without any assumption on the structure of communication network. As corollaries, we obtain a number of earlier characterization results established with the assumption of complete network (complete graph) in various specialized settings. Moreover, our characterization, as we show, can be quite different from the earlier results depending on the network structure: for example, when the network is a tree, much larger family of rules are shown to be non-manipulable. The abstract model we consider can have various special examples such as bankruptcy problems, surplus sharing problems, cost sharing problems, social choice with transferable utility, etc