Restricted Classes of Utility Functions for Simple Negotiation Schemes Sufficiency, Necessity and Maximality

We investigate the properties of an abstract negotiation framework where agents autonomously negotiate over allocations of discrete resources. In this framework, reaching an optimal allocation potentially requires very complex multilateral deals. Therefore, we are interested in identifying classes of utility functions such that any negotiation conducted by means of deals involving only a single resource at at time is bound to converge to an optimal allocation whenever all agents model their preferences using these functions. We show that the class of modular utility functions is not only sufficient (when side-payments are allowed) but also maximal in this sense. A similar result is proven in the context of negotiation without money.