Approximating Constraint-Based Utility Spaces Using Generalized Gaussian Mixture Models

  • Rafik Hadfi
  • Takayuki Ito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8861)


Complex negotiations are characterized by a particular type of utility spaces that is usually non-linear and non-monotonic. An example of such utility spaces are constraint-based utility spaces. The multitude of constraints’ shapes that could potentially be used by the negotiating agents makes any opponent modeling attempt more challenging. The same problem persists even when the agent is exploring her own utility space as to find her optimal contracts. Seeking a unified form for constraint-based utility representation might shed some light on how to tackle these problems.

In this paper, we propose to find an approximation for constraint-based preferences, used mainly in complex negotiation with non-linear utility spaces. The proposed approximation yields a compact form that unifies a whole family of constraints (Cubic, Bell, Conic, etc.). Results show that the new canonical form can in fact be an alternative representation for all known constraint-based utility functions. Additionally, it leads us to a potential parametric model that could be used for opponent modeling in complex non-linear negotiations.


Utility Function Multiagent System Optimal Contract Constant Relative Risk Aversion Utility Space 
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  1. 1.
    Azari Soufiani, H., Diao, H., Lai, Z., Parkes, D.C.: Generalized random utility models with multiple types. In: Burges, C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K. (eds.) Advances in Neural Information Processing Systems 26, pp. 73–81. Curran Associates, Inc. (2013)Google Scholar
  2. 2.
    Aziz, H.: In: Shoham, Y., Leyton-Brown, K. (eds.) Multiagent Systems: Algorithmic, Game-theoretic, and Logical Foundations. Cambridge University Press (2008); SIGACT News 41(1), 34–37 (2010)Google Scholar
  3. 3.
    Coombs, C., Avrunin, G.: Single-peaked Functions and the Theory of Preference: A Generalization of S-R Theory. Michigan mathematical psychology program, University of Michigan, Department of psychology (1976)Google Scholar
  4. 4.
    Do, C.B., Batzoglou, S.: What is the expectation maximization algorithm? Nature Biotechnology 26(8), 897–900 (2008)CrossRefGoogle Scholar
  5. 5.
    Farinelli, A., Rogers, A., Jennings, N.R.: Agent-based decentralised coordination for sensor networks using the max-sum algorithm. Journal of Autonomous Agents and Multi-Agent Systems 28(3), 337–380 (2014), CrossRefGoogle Scholar
  6. 6.
    Fujita, K., Ito, T., Klein, M.: A secure and fair negotiation protocol in highly complex utility space based on cone-constraints. In: Proceedings of the 2009 International Joint Conference on Intelligent Agent Technology (IAT 2009) (2009)Google Scholar
  7. 7.
    Hadfi, R., Ito, T.: Addressing complexity in multi-issue negotiation via utility hypergraphs. In: AAAI (2014)Google Scholar
  8. 8.
    Ito, T., Hattori, H., Klein, M.: Multi-issue negotiation protocol for agents: Exploring nonlinear utility spaces. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1347–1352 (2007)Google Scholar
  9. 9.
    Johnson, P.E.: Social Choice: Theory and Research. Quantitative Applications in the Social Sciences, vol. 123. SAGE Publications (1998)Google Scholar
  10. 10.
    Keeney, R.L., Raiffa, H.: Decisions with multiple objectives. Cambridge University Press (1993)Google Scholar
  11. 11.
    Keeney, R., Raiffa, H.: Decisions with multiple objectives preferences and value tradeoffs. Behavioral Science 39(2), 169–170 (1994)Google Scholar
  12. 12.
    Lin, R., Kraus, S., Baarslag, T., Tykhonov, D., Hindriks, K., Jonker, C.M.: Genius: An integrated environment for supporting the design of generic automated negotiators. Computational Intelligence 30(1), 48–70 (2014)CrossRefGoogle Scholar
  13. 13.
    Lopez-Carmona, M.A., Marsa-Maestre, I., De La Hoz, E., Velasco, J.R.: A region-based multi-issue negotiation protocol for nonmonotonic utility spaces. Computational Intelligence 27(2), 166–217 (2011)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Marsa-Maestre, I., Lopez-Carmona, M.A., Velasco, J.R., de la Hoz, E.: Effective bidding and deal identification for negotiations in highly nonlinear scenarios. In: Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2009, vol. 2, pp. 1057–1064. International Foundation for Autonomous Agents and Multiagent Systems, Richland (2009)Google Scholar
  15. 15.
    Marsa-Maestre, I., Lopez-Carmona, M., Carral, J., Ibanez, G.: A recursive protocol for negotiating contracts under non-monotonic preference structures. Group Decision and Negotiation 22(1), 1–43 (2013)CrossRefGoogle Scholar
  16. 16.
    von Neumann, J., Morgenstern, O.: Theory of games and economic behavior, 2nd edn. Princeton University Press, Princeton (1947)MATHGoogle Scholar
  17. 17.
    Wakker, P.P.: Explaining the characteristics of the power (crra) utility family. Health Economics 17(12), 1329–1344 (2008)CrossRefGoogle Scholar
  18. 18.
    Williams, C.R., Robu, V., Gerding, E.H., Jennings, N.R.: Using gaussian processes to optimise concession in complex negotiations against unknown opponents. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence. AAAI Press (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rafik Hadfi
    • 1
  • Takayuki Ito
    • 1
  1. 1.Department of Computer Science and EngineeringNagoya Institute of TechnologyShowa-kuJapan

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