Skip to main content
Log in

Privacy stochastic games in distributed constraint reasoning

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

In this work, we approach the issue of privacy in distributed constraint reasoning by studying how agents compromise solution quality for preserving privacy, using utility and game theory. We propose a utilitarian definition of privacy in the context of distributed constraint reasoning, detail its different implications, and present a model and solvers, as well as their properties. We then show how important steps in a distributed constraint optimization with privacy requirements can be modeled as a planning problem, and more specifically as a stochastic game. We present experiments validating the interest of our approach, according to several criteria.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arshad, M., Silaghi, M.-C.: Distributed simulated annealing. Distributed Constraint Problem Solving and Reasoning in Multi-Agent Systems, pp. 112 (2004)

  2. Bellman, R.: Dynamic Programming, 1st edn. Princeton University Press, Princeton (1957)

  3. Bernstein, D.S., Givan, R., Immerman, N., Zilberstein, S.: The complexity of decentralized control of markov decision processes. Math. Oper. Res. 27(4), 819–840 (2002)

    Article  MathSciNet  Google Scholar 

  4. Bistarelli, S., Foley, S.N., O’Sullivan, B., Santini, F.: Semiring-based frameworks for trust propagation in small-world networks and coalition formation criteria. Secur. Commun. Netw. 3(6), 595–610 (2010)

    Article  Google Scholar 

  5. Brandt, F., Conitzer, V., Lang, J., Procaccia, A.: Handbook of CoComputation Social Choice. Cambridge University Press, Cambridge (2016)

    Book  Google Scholar 

  6. Burnett, C., Norman, T.J., Sycara, K.P., Oren, N: Supporting trust assessment and decision making in coalitions. IEEE Intell. Syst. 29(4), 18–24 (2014)

    Article  Google Scholar 

  7. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plasil, F. (eds.) SOFSEM 2007: Theory and Practice of Computer Science, 33rd Conference on Current Trends in Theory and Practice of Computer Science, Harrachov, Czech Republic, 2007, Proceedings, vol. 4362, pp. 51–69. Springer (2007)

  8. Cointe, N., Bonnet, G., Boissier, O.: Ethical judgment of agents’ behaviors in multi-agent systems. In: Jonker, C.M., Marsella, S., Thangarajah, J., Tuyls, K. (eds.) Proceedings of the International Conference on Autonomous Agents & Multiagent Systems, Singapore. International Foundation for Autonomous Agents and Multiagent Systems, ACM, pp. 1106–1114 (2016)

  9. Endriss, U., Maudet, N.: Welfare engineering for multiagent systems. In: Omicini, A., Petta, P., Pitt, J. (eds.) Proceedings of the 4th International Workshop Engineering Societies in the Agent World (ESAW-2003), volume 3071 of Lecture Notes in Artificial Intelligence (LNAI), pp. 93–106. Springer (2004)

  10. Faltings, B., Léauté, T., Petcu, A.: Privacy guarantees through distributed constraint satisfaction. In: Proceedings of the 2008 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, vol. 2, pp. 350–358. IEEE Computer Society, Sydney (2008)

  11. Greenstadt, R., Grosz, B., Smith, M.D.: SSDPOP: improving the privacy of DCOP with secret sharing. In: Durfee, E.H., Yokoo, M., Huhns, M.N., Shehory, O. (eds.) Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems, pp. 171. IFAAMAS (2007)

  12. Greenstadt, R., Pearce, J.P., Bowring, E., Tambe, M.: Experimental analysis of privacy loss in dcop algorithms. In: Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS’06, pp. 1424–1426. ACM, New York (2006)

  13. Grinshpoun, T.: When you say (DCOP) privacy, what do you mean? - categorization of DCOP privacy and insights on internal constraint privacy. In: Filipe, J., Fred, A.L.N. (eds.) ICAART 2012 - Proceedings of the 4th International Conference on Agents and Artificial Intelligence, Volume 1 - Artificial Intelligence, pp. 380–386. SciTePress, Vilamoura (2012)

  14. Guo, A.Y., Lesser, V.R.: Stochastic planning for weakly-coupled distributed agents. In: Nakashima, H., Wellman, M.P., Weiss, G., Stone, P. (eds.) 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2006), pp. 326–328. ACM, Hakodate (2006)

  15. Hamila, M.A., Strugeon, E.G.-L., Mandiau, R., Mouaddib, A.I., Ghorbani, A.A., Hacid, M.-S., Yamaguchi, T.: An algorithm for multi-robot planning: Sginfinitevi. In: Huang, J.X. (ed.) Proceedings of the 2010 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2010, pp. 141–148. IEEE Computer Society Press, Toronto (2010)

  16. Hamila, M.A., Strugeon, E.G.-L., Mandiau, R., Mouaddib, A.-I.: Strategic dominance and dynamic programming for multi-agent planning - application to the multi-robot box-pushing problem. In: Filipe, Joaquim , Fred, Ana L. N. (eds.) ICAART 2012 - Proceedings of the 4th International Conference on Agents and Artificial Intelligence, Volume 2 - Agents, pp. 91–97. SciTePress, Vilamoura (2012)

  17. Hansen, E.A., Bernstein, D.S., Zilberstein, S.: Dynamic programming for partially observable stochastic games. In: McGuinness, D.L., Ferguson, G. (eds.) Proceedings of the Nineteenth National Conference on Artificial Intelligence, Sixteenth Conference on Innovative Applications of Artificial Intelligence, pp. 709–715. AAAI Press / The MIT Press, San Jose (2004)

  18. Heilman, E., Kendler, A., Zohar, A., Goldberg, S.: Eclipse attacks on bitcoin’s peer-to-peer network. In: Jung, J., Holz, T. (eds.) 24th USENIX Security Symposium, USENIX Security 15, pp. 129–144. USENIX Association, Washington (2015)

  19. Herzig, A., Lorini, E., Hübner, J.F., Vercouter, L.: A logic of trust and reputation. Log. J. IGPL 18(1), 214–244 (2010)

    Article  MathSciNet  Google Scholar 

  20. Kaelbling, L.P., Littman, M.L., Cassandra, A.R.: Planning and acting in partially observable stochastic domains. Artif. Intell. 101(1-2), 99–134 (1998)

    Article  MathSciNet  Google Scholar 

  21. Kearns, M.J., Mansour, Y., Singh, S.P.: Fast planning in stochastic games. In: Boutilier, C., Goldszmidt, M. (eds.) UAI ’00: Proceedings of the 16th Conference in Uncertainty in Artificial Intelligence, Stanford University, Stanford, pp. 309–316. Morgan Kaufmann (2000)

  22. Kumar, A., Zilberstein, S.: Dynamic programming approximations for partially observable stochastic games. In: Chad Lane, H., Guesgen, H.W. (eds.) Proceedings of the Twenty-Second International Florida Artificial Intelligence Research Society Conference. AAAI Press, Sanibel Island (2009)

  23. Léauté, T., Faltings, B.: Protecting privacy through distributed computation in multi-agent decision making. J. Artif Intell. Res. 47, 649–695 (2013)

    Article  MathSciNet  Google Scholar 

  24. Maheswaran, R.T., Tambe, M., Bowring, E., Pearce, J.P., Varakantham, P.: Taking DCOP to the real world: Efficient complete solutions for distributed multi-event scheduling. In: 3rd International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2004), pp. 310–317. IEEE Computer Society, New York (2004)

  25. Mailler, R.: Improving the privacy of the asynchronous partial overlay protocol. Multiagent Grid Syst. 8(2), 165–186 (2012)

    Article  MathSciNet  Google Scholar 

  26. Mandiau, R., Vion, J., Piechowiak, S., Monier, P.: Multi-variable distributed backtracking with sessions. Appl. Intell. 41(3), 736–758 (2014)

    Article  Google Scholar 

  27. Marsh, S.: Trust in distributed artificial intelligence, pp. 94–112. Springer, Berlin (1994)

    Google Scholar 

  28. Modi, P.J., Shen, W.-M., Tambe, M., Yokoo, M.: Adopt: Asynchronous distributed constraint optimization with quality guarantees. Artif. Intell. 161(1-2), 149–180 (2005)

    Article  MathSciNet  Google Scholar 

  29. Nash, J.F.: Non cooperative games. Ann. Math. 54(2), 286–295 (1951)

    Article  MathSciNet  Google Scholar 

  30. Ramchurn, S.D., Jennings, N.R., Sierra, C., Godo, L.: Devising A trust model for multi-agent interactions using confidence and reputation. Appl. Artif. Intell. 18(9-10), 833–852 (2004)

    Article  Google Scholar 

  31. Rapoport, A., Chammah, A.M.: Prisoner’s dilemma: A study in conflict and cooperation, vol. 165. University of Michigan Press, Ann Arbor (1965)

    Book  Google Scholar 

  32. Rapoport, A., Chammah, A.M.: The game of chicken. Amer. Behav. Sci. 10 (3), 10–28 (1966)

    Article  Google Scholar 

  33. Russell, S., Norvig, P.: Artificial intelligence: a modern approach (2010)

  34. Savaux, J., Vion, J., Piechowiak, S., Mandiau, R, Matsui, T., Hirayama, K., Yokoo, M., Elmane, S., Silaghi, M.: Stochastic game modelling for distributed constraint reasoning with privacy. In International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018, Fort Lauderdale, Florida (2018)

  35. Savaux, J., Vion, J., Piechowiak, S., Mandiau, R., Matsui, T., Hirayama, K., Yokoo, M., Elmane, S., Silaghi, M.-C.: Privacitė dans les discsp pour agents utilitaires. In: JFSMA Vingt-quatrième journėes Francophones sur les systèmes Multi-Agents, JFSMA 2016 , pp. 129–138, Rouen (2016)

  36. Savaux, J., Vion, J., Piechowiak, S., Mandiau, R., Matsui, T., Hirayama, K., Yokoo, M., Elmane, S., Silaghi, M.-C.: Discsps with privacy recast as planning problems for self-interested agents. In: IEEE/WIC/ACM International Conference on Web Intelligence (WI), pp. 359–366. IEEE (2016)

  37. Savaux, J., Vion, J., Piechowiak, S., Mandiau, R., Matsui, T., Hirayama, K., Yokoo, M., Elmane, S., Silaghi, M.: Utilitarian approach to privacy in distributed constraint optimization problems. In: Rus, V., Markov, Z. (eds.) Proceedings of the Thirtieth International Florida Artificial Intelligence Research Society Conference, FLAIRS 2017, pp. 454–459. AAAI Press, Marco Island (2017)

  38. Shapley, L. S.: Stochastic games. Proc. Natl. Acad. Sci. USA (PNAS) 39, 1095–1100 (1953)

    Article  MathSciNet  Google Scholar 

  39. Silaghi, M.-C., Abhyankar, A., Zanker, M., Barták, R.: Desk-mates (stable matching) with privacy of preferences, and a new distributed CSP framework. In: Proceedings of the Eighteenth International Florida Artificial Intelligence Research Society Conference, Clearwater Beach, pp. 671–677 (2005)

  40. Silaghi, M.-C., Faltings, B.: A comparison of distributed constraint satisfaction techniques with respect to privacy. In: Proceedings of the 3rd workshop on distributed constraints reasoning (AAMAS - DCR-02). Bologna (2002)

  41. Silaghi, M.-C., Mitra, D.: Distributed constraint satisfaction and optimization with privacy enforcement. In: 2004 IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT 2004), pp. 531–535, Beijing (2004)

  42. Silaghi, M.-C., Rajeshirke, V.: The effect of policies for selecting the solution of a discsp on privacy loss. In: Proceedings of AAMAS, pp. 1396–1397 IEEE Computer Society (2004)

  43. Silaghi, M.-C., Sam-Haroud, D., Faltings, B.: Distributed asynchronous search with private constraints. In: Rosenschein, J.S., Sierra, C., Gini, M. (eds.) AGENTS 2000 Proceedings of the fourth international conference on Autonomous agents, pp. 177–178. ACM, Barcelona (2000)

  44. Solan, E., Vieille, N.: Stochastic games. Proc. Natl. Acad. Sci. (PNAS) USA 112(45), 13743–13746 (2015)

    Article  MathSciNet  Google Scholar 

  45. Such, J.M., Espinosa, A., García-fornes, A.: A survey of privacy in multi-agent systems. Knowl. Eng. Rev. 29(3), 314–344 (2014)

    Article  Google Scholar 

  46. Tassa, T., Zivan, R., Grinshpoun, T.: Max-sum goes private. In: Yang, Q., Wooldridge, M. (eds.) Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, pp. 425–431. AAAI Press, Buenos Aires (2015)

  47. Wooldridge, M., Jennings, N.R.: Agent theories, architectures, and languages: A survey (1995)

  48. Yaich, R., Boissier, O., Picard, G., Jaillon, P.: Impact of social influence on trust management within communities of agents. Web Intell. 15(3), 251–268 (2017)

    Article  Google Scholar 

  49. Yeoh, W., Felner, A., Koenig, S.: Bnb-adopt: An asynchronous branch-and-bound dcop algorithm. In: Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems (AAMAS 2008), pp. 591–598. International Foundation for Autonomous Agents and Multiagent Systems, Estoril (2008)

  50. Yokoo, M., Durfee, E.H., Ishida, T., Kuwabara, K.: The distributed constraint satisfaction problem: Formalization and algorithms. IEEE Trans. Knowl. Data Eng. 10(5), 673–685 (1998)

    Article  Google Scholar 

  51. Yokoo, M., Durfee, E.H., Ishida, T., Kuwabara, K.: The distributed constraint satisfaction problem: Formalization and algorithms. IEEE Trans. Knowl. Data Eng. 10(5), 673–685 (1998)

    Article  Google Scholar 

  52. Yokoo, M., Ishida, T., Durfee, E.H., Kuwabara, K.: Distributed constraint satisfaction for formalizing distributed problem solving. In: Proceedings of the 12th IEEE International Conference on Distributed Computing Systems, pp. 614–621. IEEE, Yokohoma (1992)

  53. Zardi, H., Romdhane, L.B., Guessoum, Z.: Efficiently mining community structures in weighted social networks. Int. J. Data Min. Modell. Manag. IJDMMM 8(1), 32–61 (2016)

    Google Scholar 

  54. Zhang, C., Lesser, V.R.: Coordinated multi-agent reinforcement learning in networked distributed pomdps. In: Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2011, San Francisco (2011)

  55. Zhang, W., Wang, G., Wittenburg, L.: Distributed stochastic search for constraint satisfaction and optimization: Parallelism, phase transitions and performance. In: Proceedings of AAAI Workshop on Probabilistic Approaches in Search, Alberta, Canada (2002)

  56. Zivan, R., Meisels, A.: Synchronous vs asynchronous search on discsps. In: Proceedings of the First European Workshop on Multi-Agent Systems (EUMAS), Oxford, England (2003)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Julien Savaux.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Savaux, J., Vion, J., Piechowiak, S. et al. Privacy stochastic games in distributed constraint reasoning. Ann Math Artif Intell 88, 691–715 (2020). https://doi.org/10.1007/s10472-019-09628-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-019-09628-8

Keywords

Mathematics Subject Classification (2010)

Navigation