On optimal outcomes of negotiations over resources

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

“…We conclude this background section by recalling two important results [12,7]: the first one makes explicit the connection between the local decisions of agents and the global behaviour of the system, and the second one is the fundamental convergence theorem for this negotiation framework.…”

“…This holds when any type of deals are allowed. Only the slightest restriction on the number of agents and/or resources allowed to be involved in a deal would prevent this result [7].…”

“…While Theorem 1 shows that, in principle, it is always possible to negotiate an allocation of resources that is optimal from a social point of view, deals involving any number of agents and resources may be required to do so [12,7]. In particular, the most basic type of deal, which involves moving a single resource from one agent to another and which is the type of deal implemented in most systems realising a kind of Contract Net protocol [13], is certainly not sufficient for negotiation between agents that are not only rational but also myopic.…”

“…Under this perspective, a relevant result is due to Endriss et al [7], who show that rational 1-deals are sufficient to guarantee outcomes with maximal social welfare in case all agents use additive utility functions. 3 We are going to prove a slight generalisation of this result in the next section.…”

“…In this case, the system designer will typically seek to set up the system in such way that it guarantees desirable properties, without directly interfering in the negotiation process itself. In this paper we will make use of such an abstract negotiation framework investigated by a number of authors [12,7,6].…”