Modeling complex nonlinear utility spaces using utility hyper-graphs

There has been an increasing interest in automated negotiation and particularly negotiations that involve interdependent issues, known to yield complex nonlinear utility spaces. However, none of the proposed models was able to tackle the scaling problem as it commonly arises in realistic consensus making situations. In this paper we address this point by proposing a compact representation that minimizes the search complexity in this type of utility spaces. Our representation allows a modular decomposition of the issues and the constraints by mapping the utility space into an issue-constraint hyper-graph with the underlying interdependencies. Exploring the utility space reduces then to a message passing mechanism along the hyper-edges by means of utility propagation. We experimentally evaluate the model using parameterized random nonlinear utility spaces, showing that our mechanism can handle a large family of complex utility spaces by finding the optimal contracts, outperforming previous sampling-based approaches.