Document Open Access Logo

Communication Complexity of Correlated Equilibrium with Small Support

Authors Anat Ganor, Karthik C. S.

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2018.12.pdf
  • Filesize: 0.51 MB
  • 16 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Exact and approximate computation of equilibria
Keywords
  • Correlated equilibrium
  • Nash equilibrium
  • Communication complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We define a two-player N x N game called the 2-cycle game, that has a unique pure Nash equilibrium which is also the only correlated equilibrium of the game. In this game, every 1/poly(N)-approximate correlated equilibrium is concentrated on the pure Nash equilibrium. We show that the randomized communication complexity of finding any 1/poly(N)-approximate correlated equilibrium of the game is Omega(N). For small approximation values, our lower bound answers an open question of Babichenko and Rubinstein (STOC 2017).

Cite As Get BibTex

Anat Ganor and Karthik C. S.. Communication Complexity of Correlated Equilibrium with Small Support. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.12

Author Details

Anat Ganor
  • Tel Aviv University, Tel Aviv, Israel
Karthik C. S.
  • Weizmann Institute of Science, Rehovot, Israel

Funding

  • Ganor, Anat: The research leading to these results has received funding from the Israel Science Foundation (grant number 552/16) and the I-CORE Program of the planning and budgeting committee and The Israel Science Foundation (grant number 4/11).
  • C. S., Karthik: This work was supported by Irit Dinur’s ERC-CoG grant 772839 and ISF-UGC grant 1399/14.

References

  1. Robert Aumann. Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics, 1(1):67-96, 1974. Google Scholar
  2. Robert Aumann. Correlated equilibrium as an expression of bayesian rationality. Econometrica, 55(1):1-18, 1987. Google Scholar
  3. László Babai, Peter Frankl, and Janos Simon. Complexity classes in communication complexity theory (preliminary version). In FOCS, pages 337-347, 1986. Google Scholar
  4. Yakov Babichenko. private communication, 2017. Google Scholar
  5. Yakov Babichenko, Siddharth Barman, and Ron Peretz. Empirical distribution of equilibrium play and its testing application. Math. Oper. Res., 42(1):15-29, 2017. URL: http://dx.doi.org/10.1287/moor.2016.0794.
  6. Yakov Babichenko and Aviad Rubinstein. Communication complexity of approximate Nash equilibria. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 878-889, 2017. Google Scholar
  7. Siddharth Barman and Katrina Ligett. Finding any nontrivial coarse correlated equilibrium is hard. In Proceedings of the Sixteenth ACM Conference on Economics and Computation, EC '15, Portland, OR, USA, June 15-19, 2015, pages 815-816, 2015. URL: http://dx.doi.org/10.1145/2764468.2764497.
  8. Vincent Conitzer and Tuomas Sandholm. Communication complexity as a lower bound for learning in games. In Machine Learning, Proceedings of the Twenty-first International Conference (ICML 2004), Banff, Alberta, Canada, July 4-8, 2004, 2004. URL: http://dx.doi.org/10.1145/1015330.1015351.
  9. Artur Czumaj, Argyrios Deligkas, Michail Fasoulakis, John Fearnley, Marcin Jurdzinski, and Rahul Savani. Distributed methods for computing approximate equilibria. In Web and Internet Economics - 12th International Conference, WINE 2016, Montreal, Canada, December 11-14, 2016, Proceedings, pages 15-28, 2016. URL: http://dx.doi.org/10.1007/978-3-662-54110-4_2.
  10. John Fearnley, Martin Gairing, Paul W. Goldberg, and Rahul Savani. Learning equilibria of games via payoff queries. Journal of Machine Learning Research, 16:1305-1344, 2015. URL: http://dl.acm.org/citation.cfm?id=2886792.
  11. John Fearnley and Rahul Savani. Finding approximate Nash equilibria of bimatrix games via payoff queries. ACM Trans. Economics and Comput., 4(4):25:1-25:19, 2016. URL: http://dx.doi.org/10.1145/2956579.
  12. Itzhak Gilboa and Eitan Zemel. Nash and correlated equilibria: Some complexity considerations. Games and Economic Behavior, 1(1):80-93, 1989. URL: http://dx.doi.org/10.1016/0899-8256(89)90006-7.
  13. Paul Goldberg. Surveys in Combinatorics 2011. London Mathematical Society Lecture Note Series, 2011. Google Scholar
  14. Paul W. Goldberg and Arnoud Pastink. On the communication complexity of approximate Nash equilibria. Games and Economic Behavior, 85:19-31, 2014. URL: http://dx.doi.org/10.1016/j.geb.2014.01.009.
  15. Paul W. Goldberg and Aaron Roth. Bounds for the query complexity of approximate equilibria. In ACM Conference on Economics and Computation, EC '14, Stanford , CA, USA, June 8-12, 2014, pages 639-656, 2014. URL: http://dx.doi.org/10.1145/2600057.2602845.
  16. Sergiu Hart and Yishay Mansour. How long to equilibrium? the communication complexity of uncoupled equilibrium procedures. Games and Economic Behavior, 69(1):107-126, 2010. URL: http://dx.doi.org/10.1016/j.geb.2007.12.002.
  17. Sergiu Hart and Andreu Mas-Colell. Uncoupled dynamics do not lead to Nash equilibrium. American Economic Review, 93(5):1830-1836, 2003. Google Scholar
  18. Sergiu Hart and Andreu Mas-Colell. Stochastic uncoupled dynamics and Nash equilibrium. Games and Economic Behavior, 57(2):286-303, 2006. Google Scholar
  19. Sergiu Hart and Andreu Mas-Colell. Simple Adaptive Strategies:From Regret-Matching to Uncoupled Dynamics. World Scientific Publishing Co. Pte. Ltd., 2013. Google Scholar
  20. Sergiu Hart and David Schmeidler. Existence of correlated equilibria. Math. Oper. Res., 14(1):18-25, 1989. URL: http://dx.doi.org/10.1287/moor.14.1.18.
  21. Albert Xin Jiang and Kevin Leyton-Brown. Polynomial-time computation of exact correlated equilibrium in compact games. Games and Economic Behavior, 91:347-359, 2015. URL: http://dx.doi.org/10.1016/j.geb.2013.02.002.
  22. Ehud Kalai and Ehud Lehrer. Rational learning leads to nash equilibrium. Econometrica, 61(5):1019-45, 1993. Google Scholar
  23. Bala Kalyanasundaram and Georg Schnitger. The probabilistic communication complexity of set intersection. SIAM J. Discrete Math., 5(4):545-557, 1992. Google Scholar
  24. Young Kun Ko and Ariel Schvartzman. Bounds for the communication complexity of two-player approximate correlated equilibria. Electronic Colloquium on Computational Complexity (ECCC), 24:71, 2017. URL: https://eccc.weizmann.ac.il/report/2017/071.
  25. Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, New York, NY, USA, 1997. Google Scholar
  26. Troy Lee and Adi Shraibman. Lower bounds in communication complexity. Foundations and Trends in Theoretical Computer Science, 3(4):263-398, 2009. Google Scholar
  27. Moni Naor. private communication, 2017. Google Scholar
  28. J.F. Nash. Non-cooperative games. Annals of Mathematics, 54(2):286-295, 1951. Google Scholar
  29. Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V Vazirani. Algorithmic Game Theory. Cambridge University Press, New York, NY, USA, 2007. Google Scholar
  30. Christos H. Papadimitriou and Tim Roughgarden. Computing correlated equilibria in multi-player games. J. ACM, 55(3):14:1-14:29, 2008. URL: http://dx.doi.org/10.1145/1379759.1379762.
  31. Alexander A. Razborov. On the distributional complexity of disjointness. Theor. Comput. Sci., 106(2):385-390, 1992. Google Scholar
  32. Tim Roughgarden. Computing equilibria: a computational complexity perspective. Economic Theory, 42(1):193-236, 2010. URL: http://dx.doi.org/10.1007/s00199-009-0448-y.
  33. Tim Roughgarden. Communication complexity (for algorithm designers). Foundations and Trends in Theoretical Computer Science, 11(3-4):217-404, 2016. URL: http://dx.doi.org/10.1561/0400000076.
  34. Tim Roughgarden. Twenty Lectures on Algorithmic Game Theory. Cambridge University Press, 2016. Google Scholar
  35. Tim Roughgarden and Omri Weinstein. On the communication complexity of approximate fixed points. In IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, 9-11 October 2016, Hyatt Regency, New Brunswick, New Jersey, USA, pages 229-238, 2016. URL: http://dx.doi.org/10.1109/FOCS.2016.32.
  36. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of the 11h Annual ACM Symposium on Theory of Computing, April 30 - May 2, 1979, Atlanta, Georgia, USA, pages 209-213, 1979. Google Scholar
  37. H. Peyton Young. H. peyton young, , strategic learning and its limits (2004) oxford univ. press 165 pages. Games and Economic Behavior, 63(1):417-420, 2004. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact