On the complexity of utility hypergraphs

Abstract

We provide a new representation for nonlinear utility spaces by adopting a modular decomposition of the issues and the constraints. This is based on the intuition that constraint-based utility spaces are nonlinear with respect to issues, but linear with respect to the constraints. The result is a mapping from a utility space into an issue-constraint hypergraph with the underling interdependencies. Exploring the utility space reduces then to a message passing mechanism along the hyperedges by means of utility propagation. The optimal contracts are efficiently found using a variation of the Max-Sum algorithm. We experimentally evaluate the model using parameterized random nonlinear utility spaces, showing that it can handle a large family of complex utility spaces using several exploration strategies. We also evaluate the complexity of the generated utility spaces using the entropy and establish an optimal search strategy allowing a better scaling of the model.