Proposal-Based Negotiation in Convex Regions

In this work we analyze negotiation between two partially cooperative agents, which are supposed to find an agreement which satisfies both of them minimizing the number of iterations. Our goal is to understand the role that reasoning can play in speeding up the search for an agreement. We do not put any limit on the number of shared variables and constraints, and analyze the negotiation problem under the hypothesis that the admissibility regions for each agent are convex. Under such a framework, we show how an agent can perform a sophisticated form of reasoning, which can be formalized by means of projections on the other agent’s proposals. The main technical result of this paper is that projections can be very effective in speeding up negotiation; in particular, we show by means of several examples that reasoning about the other agent’s reasoning using projections allows a protocol which is, in some cases, very efficient. We also investigate the intrinsic limits of the methodology, showing that there are some worst-case scenarios in which the number of exchanged proposals is exponential both in the number of variables and in the number of constraints.