Complex Multi-Issue Negotiation Using Utility Hyper-Graphs

We propose to handle the complexity of utility spaces used in multi-issue negotiation by adopting a new representation that allows a modular decomposition of the issues and the constraints. This is based on the idea that a constraint-based utility space is nonlinear with respect to issues, but linear with respect to the constraints. This allows us to rigorously map the utility space into an issue-constraint hyper-graph. Exploring the utility space reduces then to a message passing mechanism along the hyper-edges of the hyper-graph by means of utility propagation. Optimal contracts are found efficiently using a variation of the Max-Sum algorithm. We evaluate the model experimentally using parameterized nonlinear utility spaces, showing that it can handle a large family of complex utility spaces by finding optimal contracts, outperforming previous sampling-based approaches. We also evaluate the model in a negotiation setting. We show that under high complexity, social welfare could be greater than the sum of the individual agents’ best utilities.