Coalitional Manipulation on Networks

We consider an abstract model of division problems where each agent is identi- fied by a characteristic vector. Agents are situated on a network (a non-directed graph) and any connected coalition can reallocate members¡¯ characteristics (e.g. reallocation of claims in bankruptcy problems). A reallocation-proof rule prevents any coalition from benefiting, in terms of its total award, through a reallocation. We offer a full characterization of reallocation-proof rules without any assumption on the network structure. This result yields a variety of useful corollaries for specific networks such as the complete network, trees, networks without a ¡°bridge¡± etc. Our model has various special examples such as bankruptcy, surplus sharing, cost sharing, income redistribution, social choice with transferable utility, etc.