Notre Dame Journal of Formal Logic

Functional Dependence in Strategic Games

Kristine Harjes and Pavel Naumov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The article studies properties of functional dependencies between strategies of players in Nash equilibria of multiplayer strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for payoff functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.

Article information

Source
Notre Dame J. Formal Logic, Volume 57, Number 3 (2016), 341-353.

Dates
Received: 20 March 2013
Accepted: 29 October 2013
First available in Project Euclid: 25 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1456413345

Digital Object Identifier
doi:10.1215/00294527-3479096

Mathematical Reviews number (MathSciNet)
MR3521484

Zentralblatt MATH identifier
06621293

Subjects
Primary: 03B80: Other applications of logic

Keywords
strategic games functional dependency axiomatization completeness

Citation

Harjes, Kristine; Naumov, Pavel. Functional Dependence in Strategic Games. Notre Dame J. Formal Logic 57 (2016), no. 3, 341--353. doi:10.1215/00294527-3479096. https://projecteuclid.org/euclid.ndjfl/1456413345


Export citation

References

  • [1] Armstrong, W. W., “Dependency structures of data base relationships,” pp. 580–83 in Information Processing 74 (Proc. IFIP Congress, Stockholm, 1974), North-Holland, Amsterdam, 1974.
  • [2] Beeri, C., R. Fagin, and J. H. Howard, “A complete axiomatization for functional and multivalued dependencies in database relations,” pp. 47–61 in SIGMOD ’77: Proceedings of the 1977 ACM SIGMOD International Conference on Management of Data, ACM, New York, 1977.
  • [3] Elkind, E., L. A. Goldberg, and P. W. Goldberg, “Nash equilibria in graphical games on trees revisited,” pp. 100–109 in ACM Conference on Electronic Commerce, ACM, New York, 2006.
  • [4] Elkind, E., L. A. Goldberg, and P. W. Goldberg, “Computing good Nash equilibria in graphical games,” pp. 162–71 in ACM Conference on Electronic Commerce, edited by J. K. MacKie-Mason, D. C. Parkes, and P. Resnick, ACM, New York, 2007.
  • [5] Garcia-Molina, H., J. D. Ullman, and J. Widom, Database Systems: The Complete Book, 2nd ed., Pearson, Upper Saddle River, N.J., 2009.
  • [6] Harjes, K., and P. Naumov, “Functional dependence in strategic games,” preprint, arXiv:1302.0447v1 [math.LO].
  • [7] Kearns, M. J., M. L. Littman, and S. P. Singh, “Graphical models for game theory,” pp. 253–60 in Conference in Uncertainty in Artificial Intelligence, edited by J. S. Breese and D. Koller, Morgan Kaufmann, San Francisco, 2001.
  • [8] Littman, M. L., M. J. Kearns, and S. P. Singh, “An efficient, exact algorithm for solving tree-structured graphical games,” pp. 817–23 in Advances in Neural Information Processing Systems 14 (NIPS, 2001), edited by T. G. Dietterich, S. Becker, and Z. Ghahramani, MIT Press, Cambridge, Mass., 2001.
  • [9] More, S. M., and P. Naumov, “The functional dependence relation on hypergraphs of secrets,” pp. 29–40 in Computational Logic in Multi-Agent Systems, edited by J. Leite, P. Torroni, T. Ågotnes, G. Boella, and L. van der Torre, vol. 6814 of Lecture Notes in Computer Science, Springer, Berlin, 2011.
  • [10] Naumov, P., and B. Nicholls, “Rationally functional dependence,” Journal of Philosophical Logic, vol. 43 (2014), pp. 603–16.