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\(\hbox {NB}^{3}\): a multilateral negotiation algorithm for large, non-linear agreement spaces with limited time

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Abstract

Existing work on automated negotiations has mainly focused on bilateral negotiations with linear utility functions. It is often assumed that all possible agreements and their utility values are given beforehand. Most real-world negotiations however are much more complex. We introduce a new family of negotiation algorithms that is applicable to domains with many agents, an intractably large space of possible agreements, non-linear utility functions and limited time so an exhaustive search for the best proposals is not feasible. We assume that agents are selfish and cannot be blindly trusted, so the algorithm does not rely on any mediator. This family of algorithms is called \(\hbox {NB}^{3}\) and applies heuristic Branch & Bound search to find good proposals. Search and negotiation happen simultaneously and therefore strongly influence each other. It applies a new time-based negotiation strategy that considers two utility aspiration levels: one for the agent itself and one for its opponents. Also, we introduce a negotiation protocol that imposes almost no restrictions and is therefore better applicable to negotiations with humans. We present the Negotiating Salesmen Problem (NSP): a variant of the Traveling Salesman Problem with multiple negotiating agents, as a test case. We describe an implementation of \(\hbox {NB}^{3}\) designed for the NSP and present the results of experiments with this implementation. We conclude that the algorithm is able to decrease the costs of the agents significantly, that the heuristic search is efficient and that the algorithm scales well with increasing complexity of the problem.

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Notes

  1. In this paper we use Greek letters to indicate specific elements of the set \(A\) (i.e. they are the names of the agents), while we use Latin letters as variables over the set \(A\). The letter \(\epsilon \) however is used to refer to world states, so it is not the name of any agent.

  2. As mentioned before, to keep the discussion simple we assume that the order in which actions are taken is irrelevant for the outcome of the state of the world, even though our algorithm would work just as well without this restriction. Therefore, we see a plan as a set of actions, rather than a sequence of actions. So a set of plans is a set of sets of actions.

  3. We will not discuss how it could obtain such a model, because there are many ways to do this and depends on the domain. In the case of NSP this is simple, because it is known that each agent wants to minimize its path.

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Acknowledgments

Supported by the Agreement Technologies CONSOLIDER Project, Contract CSD2007-0022 and INGENIO 2010 and CHIST-ERA Project ACE and the Spanish Ministry of Education and Science TIN2010-16306 Project CBIT and EU Project 318770 PRAISE and Project PACES; EPSRC EP/J012149/1.

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  1. Artificial Intelligence Research Institute, IIIA-CSIC, Campus de la Universitat Autònoma de Barcelona, Bellaterra, Catalonia, Spain

    Dave de Jonge & Carles Sierra

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Correspondence to Dave de Jonge.

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de Jonge, D., Sierra, C. \(\hbox {NB}^{3}\): a multilateral negotiation algorithm for large, non-linear agreement spaces with limited time. Auton Agent Multi-Agent Syst 29, 896–942 (2015). https://doi.org/10.1007/s10458-014-9271-3

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