Abstract
We investigate the properties of an abstract negotiation framework where agents autonomously negotiate over allocations of indivisible resources. In this framework, reaching an allocation that is optimal may require very complex multilateral deals. Therefore, we are interested in identifying classes of valuation functions such that any negotiation conducted by means of deals involving only a single resource at a time is bound to converge to an optimal allocation whenever all agents model their preferences using these functions. In the case of negotiation with monetary side payments amongst self-interested but myopic agents, the class of modular valuation functions turns out to be such a class. That is, modularity is a sufficient condition for convergence in this framework. We also show that modularity is not a necessary condition. Indeed, there can be no condition on individual valuation functions that would be both necessary and sufficient in this sense. Evaluating conditions formulated with respect to the whole profile of valuation functions used by the agents in the system would be possible in theory, but turns out to be computationally intractable in practice. Our main result shows that the class of modular functions is maximal in the sense that no strictly larger class of valuation functions would still guarantee an optimal outcome of negotiation, even when we permit more general bilateral deals. We also establish similar results in the context of negotiation without side payments.
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Andersson, M., & Sandholm, T. W. (1999). Time-quality tradeoffs in reallocative negotiation with combinatorial contract types. In Proceedings of the 16th national conference on artificial intelligence (AAAI-1999). MIT Press.
Arrow, K.J., Sen, A.K., Suzumura, K. (eds) (2002) Handbook of social choice and welfare, Vol. 1. North-Holland, Amsterdam
Ausiello G., Crescenzi P., Gambosi G., Kann V., Marchetti-Spaccamela A., Protasi M. (1999) Complexity and approximation: Combinatorial optimization problems and their approximability properties. Springer-Verlag, Berlin
Bachrach, Y., & Rosenschein, J. S. (2008). Distributed multiagent resource allocation in diminishing marginal return domains. In Proceedings of the 7th international joint conference on autonomous agents and multiagent systems (AAMAS-2008) (pp. 1103–1110). Honolulu, USA: IFAAMAS.
Boros E., Hammer P.L. (2002) Pseudo-boolean optimization. Discrete Applied Mathematics 123(1–3): 155–225
Boutilier, C., & Hoos, H. H. (2001). Bidding languages for combinatorial auctions. In Proceedings of the 17th international joint conference on artificial intelligence (IJCAI-2001) (pp. 1211–1217). Seattle, WA, USA: Morgan Kaufmann.
Chevaleyre Y., Dunne P.E., Endriss U., Lang J., Lemaître M., Maudet N., Padget J., Phelps S., Rodríguez-Aguilar J.A., Sousa P. (2006) Issues in multiagent resource allocation. Informatica 30: 3–31
Chevaleyre Y., Endriss U., Estivie S., Maudet N. (2008) Multiagent resource allocation in k-additive domains: Preference representation and complexity. Annals of Operations Research 163(1): 49–62
Chevaleyre, Y., Endriss, U., & Maudet, N. (2005). On maximal classes of utility functions for efficient one-to-one negotiation. In Proceedings of the 19th international joint conference on artificial intelligence (IJCAI-2005) (pp. 941–946). Los Altos, CA, USA: Morgan Kaufmann Publishers.
Cramton, P., Shoham, Y., Steinberg, R. (eds) (2006) Combinatorial auctions. MIT Press, Cambridge
Dunne P.E., Chevaleyre Y. (2008) The complexity of deciding reachability properties of distributed negotiation schemes. Theoretical Computer Science 396(1–3): 113–144
Dunne P.E., Wooldridge M., Laurence M. (2005) The complexity of contract negotiation. Artificial Intelligence 164(1–2): 23–46
Endriss U., Maudet N., Sadri F., Toni F. (2006) Negotiating socially optimal allocations of resources. Journal of Artificial Intelligence Research 25: 315–348
Faltings B., Yokoo M. (2005) Introduction: Special issue on distributed constraint satisfaction. Artificial Intelligence 161(1–2): 1–5
Galstyan A., Czajkowski K., Lerman K. (2005) Resource allocation in the Grid with learning agents. Journal of Grid Computing 3(1–2): 91–100
Garey M.R., Johnson D.S. (1979) Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Co., New York
Giovannucci, A., Rodríguez-Aguilar, J. A., Reyes, A., Noria, F. X., & Cerquides, J. (2004). Towards automated procurement via agent-aware negotiation support. In Proceedings of the 3rd international joint conference on autonomous agents and multiagent systems (AAMAS-2004) (pp. 244–253). New York: ACM Press.
Grabisch M. (1997) k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92: 167–189
Kraus S. (2001) Strategic negotiation in multiagent environments. MIT Press, Cambridge
Ladner R.E., Lynch N.A., Selman A.L. (1975) A comparison of polynomial time reducibilities. Theoretical Computer Science 1(2): 103–123
Lemaître, M., Verfaillie, G., & Bataille, N. (1999). Exploiting a common property resource under a fairness constraint: A case study. In Proceedings of the 16th international joint conference on artificial intelligence (IJCAI-1999). Los Altos, CA, USA: Morgan Kaufmann Publishers.
Moulin H. (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge, UK
Narumanchi M.V., Vidal J.M. (2006) Algorithms for distributed winner determination in combinatorial auctions. In: La Poutré H., Sadeh N., Janson S. (eds) Agent-mediated electronic commerce. designing trading agents and mechanisms. Springer-Verlag, Berlin, pp 43–56
Nisan N. et al (2006) Bidding languages for combinatorial auctions. In: Cramton P. (eds) Combinatorial auctions. MIT Press, Cambridge, MA
Parkes, D., & Shneidman, J. (2004). Distributed implementations of Vickrey-Clarke-Groves mechanisms. In Proceedings of the 3rd international joint conference on autonomous agents and multiagent systems (AAMAS-2004) (pp. 261–268). New York: ACM Press.
Petcu, A., Faltings, B., & Parkes, D. (2006). MDPOP: Faithful distributed implementation of efficient social choice problems. In Proceedings of the 5th international joint conference on autonomous agents and multiagent systems (AAMAS-2006) (pp. 1397–1404). New York: ACM Press.
Rosenschein J.S., Zlotkin G. (1994) Rules of encounter. MIT Press, Cambridge, MA
Rothkopf M.H., Pekec̆ A., Harstad R.M. (1998) Computationally manageable combinational auctions. Management Science 44(8): 1131–1147
Saha, S., & Sen, S. (2007). An efficient protocol for negotiation over multiple indivisible resources. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI-2007) (pp. 1494–1499). Hyderabad, India.
Sandholm, T. W. (1998). Contract types for satisficing task allocation: I. Theoretical results. In Proceedings of the AAAI spring symposium: Satisficing models.
Sandholm T.W. (1999) Distributed rational decision making. In: Weiß G. (eds) Multiagent systems: A modern approach to distributed artificial intelligence. MIT Press, Cambridge, MA, pp 201–258
Sandholm, T. W., Suri, S., Gilpin, A., & Levine, D. (2002). Winner determination in combinatorial auction generalizations. In Proceedings of the 1st international joint conference on autonomous agents and multiagent systems (AAMAS-2002). New York: ACM Press.
Smith R.G. (1980) The contract net protocol: High-level communication and control in a distributed problem solver. IEEE Transactions on Computers C-29(12): 1104–1113
Uckelman, J., Chevaleyre, Y., Endriss, U., & Lang, J. (2009). Representing utility functions via weighted goals. Mathematical Logic Quarterly (in press).
Vidal, J. M. (2006). Multiagent coordination using a distributed combinatorial auction. In Proceedings of the AAAI workshop on auction mechanisms for robot coordination.
Wooldridge M. (2002) An introduction to multiagent systems. Wiley, West Sussex, England
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We would like to thank the reviewers of this paper and its earlier incarnations for their very helpful feedback.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Chevaleyre, Y., Endriss, U. & Maudet, N. Simple negotiation schemes for agents with simple preferences: sufficiency, necessity and maximality. Auton Agent Multi-Agent Syst 20, 234–259 (2010). https://doi.org/10.1007/s10458-009-9088-7
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DOI: https://doi.org/10.1007/s10458-009-9088-7