Logic-based automated multi-issue bilateral negotiation in peer-to-peer e-marketplaces

Abstract

We present a novel logic-based framework to automate multi-issue bilateral negotiation in e-commerce settings. The approach exploits logic as communication language among agents, and optimization techniques in order to find Pareto-efficient agreements. We introduce $${\mathcal{P}}({\mathcal{N}})$$ , a propositional logic extended with concrete domains, which allows one to model relations among issues (both numerical and non-numerical ones) via logical entailment, differently from well-known approaches that describe issues as uncorrelated. Through $${\mathcal{P}}({\mathcal{N}})$$ it is possible to represent buyer's request, seller's supply and their respective preferences as formulas endowed with a formal semantics, e.g., if I spend more than 30000 � for a sedan then I want more than a two-years warranty and a GPS system included. We mix logic and utility theory in order to express preferences in a qualitative and quantitative way. We illustrate the theoretical framework, the logical language, the one-shot negotiation protocol we adopt, and show we are able to compute Pareto-efficient outcomes, using a mediator to solve an optimization problem. We prove the computational adequacy of our method by studying the complexity of the problem of finding Pareto-efficient solutions in our setting.