Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus

We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new values extending the Shapley value and the Banzhaf value, respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in today's fully integrated societies.