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An architectural view of game theoretic control

Published:03 January 2011Publication History
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Abstract

Game-theoretic control is a promising new approach for distributed resource allocation. In this paper, we describe how game-theoretic control can be viewed as having an intrinsic layered architecture, which provides a modularization that simplifies the control design. We illustrate this architectural view by presenting details about one particular instantiation using potential games as an interface. This example serves to highlight the strengths and limitations of the proposed architecture while also illustrating the relationship between game-theoretic control and other existing approaches to distributed resource allocation.

References

  1. S. Adlakha, R. Johari, G. Weintraub, and A. Goldsmith. Oblivious equilibrium: an approximation to large population dynamic games with concave utility. In Game Theory for Networks, pages 68--69, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. T. Alpcan, L. Pavel, and N. Stefanovic. A control theoretic approach to noncooperative game design. In IEEE CDC, pages 8575--8580, 2009.Google ScholarGoogle ScholarCross RefCross Ref
  3. E. Altman and Z. Altman. S-modular games and power control in wireless networks. Transactions on Automatic Control, 48(5):839--842, 2003.Google ScholarGoogle ScholarCross RefCross Ref
  4. E. Altman, T. Boulogne, R. El-Azouzi, T. Jiménez, and L. Wynter. A survey on networking games in telecommunications. Computers and Operations Research, 33(2):286--311, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. E. Altman, R. El-Azouzi, and T. Jiménez. Slotted ALOHA as a game with partial information. Computer Networks, 45(6):701--713, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. L. Blume. The statistical mechanics of strategic interaction. Games and Economic Behavior, 5:387--424, 1993.Google ScholarGoogle ScholarCross RefCross Ref
  7. E. Campos-Náñez, E. Garcia, and C. Li. A game-theoretic approach to efficient power management in sensor networks. Operations Research, 56(3):552--561, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. C. G. Cassandras and W. Li. Sensor networks and cooperative control. European Journal of Control, 11(4-5):436--463, 2005.Google ScholarGoogle ScholarCross RefCross Ref
  9. A. Chapman, A. Rogers, and N. R. Jennings. Benchmarking hybrid algorithms for distributed constraint optimization games. In ACM OptMAS, pages 1--11, 2008.Google ScholarGoogle Scholar
  10. H.-L. Chen, T. Roughgarden, and G. Valiant. Designing networks with good equilibria. In ACM-SIAM SODA, pages 854--863, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. V. Conitzer and T. Sandholm. Computing shapley values, manipulating value division schemes, and checking core membership in multi-issue domains. In AAAI, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. M. Csete and J. C. Doyle. Bow ties, metabolism and disease. Trends in Biotechnology", 22(9):446--450, 2004.Google ScholarGoogle Scholar
  13. P. Dubey, O. Haimanko, and A. Zapechelnyuk. Strategic complements and substitutes, and potential games. Games and Economic Behavior, 54(1):77--94, 2006.Google ScholarGoogle ScholarCross RefCross Ref
  14. D. Falomari, N. Mandayam, D. Goodman, and V. Shah. A new framework for power control in wireless data networks: games, utility, and pricing. In Wireless Multimedia Network Technologies, pages 289--310. 1999.Google ScholarGoogle Scholar
  15. D. Fudenberg and D. Levine. The Theory of Learning in Games. MIT Press, Cambridge, MA, 1998.Google ScholarGoogle Scholar
  16. A. Garcia, D. Reaume, and R. L. Smith. Fictitious play for finding system optimal routings in dynamic traffic networks. Transportation Research Part B: Methodological, 34(2):147--156, 2000.Google ScholarGoogle ScholarCross RefCross Ref
  17. B. Kauffmann, F. Baccelli, A. Chaintreau, V. Mhatre, K. Papagiannaki, and C. Diot. Measurement-based self organization of interfering 802.11 wireless access networks. In IEEE INFOCOM, pages 1451--1459, 2007.Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. In ACM KDD, pages 137--146, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. R. S. Komali and A. B. MacKenzie. Distributed topology control in ad-hoc networks: a game theoretic perspective. In IEEE CCNC, pages 563--568, 2006.Google ScholarGoogle ScholarCross RefCross Ref
  20. J. F. Kurose and K. W. Ross. Computer networking: a top-down approach. Addison-Wesley, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. L. E. Li, J. Y. Halpern, P. Bahl, Y.-M. Wang, and R. Wattenhofer. A cone-based distributed topology-control algorithm for wireless multi-hop networks. Transactions on Networking, 13(1):147--159, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. J. R. Marden, G. Arslan, and J. S. Shamma. Regret based dynamics: convergence in weakly acyclic games. In ACM AAMAS, pages 1--8, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. J. R. Marden, G. Arslan, and J. S. Shamma. Joint strategy fictitious play with inertia for potential games. Transactions on Automatic Control, 54(2):208--220, Feb 2009.Google ScholarGoogle ScholarCross RefCross Ref
  24. J. R. Marden and J. S. Shamma. Revisiting log-linear learning: Asynchrony, completeness and a payoff-based implementation,. In Under submission.Google ScholarGoogle Scholar
  25. J. R. Marden and A. Wierman. Distributed welfare games. Under submission.Google ScholarGoogle Scholar
  26. J. R. Marden and A. Wierman. Overcoming limitations of game-theoretic distributed control. In IEEE CDC, pages 6466--6471, 2009.Google ScholarGoogle ScholarCross RefCross Ref
  27. V. Mhatre, K. Papagiannaki, and F. Baccelli. Interference mitigation through power control in high density 802.11 wlans. In IEEE INFOCOM, pages 535--543, 2007.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. A. Mishra, V. Shrivastava, D. Agrawal, S. Banerjee, and S. Ganguly. Distributed channel management in uncoordinated wireless environments. In MOBICOM, pages 170--181, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. D. Monderer and L. S. Shapley. Fictitious play property for games with identical interests. Economic Theory, 68(1):258--265, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  30. Nat. Research Council Comm. on the Internet in the Evolving Info. Infrastructure. The Internet's coming of age, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. N. Nisan, T. Roughgarden, E. Tardos, and V. V. Vazirani. Algorithmic game theory. Cambridge University Press, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. P. Parag, S. Shakkottai, and J.-F. Chamberland. Value-aware resource allocation for service guarantees in networks. In IEEE INFOCOM, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. L. Pavel. An extension of duality to a game-theoretic framework. Automatica, 43:226237, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. A. Rantzer. Distributed control using decompositions and games. In IEEE CDC, 2008.Google ScholarGoogle Scholar
  35. W. H. Sandholm. Potential games with continuous player sets. Journal of Economic Theory, 97(1):81--108, 2001.Google ScholarGoogle ScholarCross RefCross Ref
  36. G. Scutari, D. P. Palomar, and J. Pang. Flexible design of cognitive radio wireless systems: from game theory to variational inequality theory. IEEE Signal Processing Magazine, 26(5):107--123, September 2009.Google ScholarGoogle ScholarCross RefCross Ref
  37. D. Shah and J. Shin. Dynamics in congestion games. In ACM SIGMETRICS/Performance, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. J. Shamma and G. Arslan. Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria. IEEE Trans. on Automatic Control, 50(3):312--327, 2005.Google ScholarGoogle ScholarCross RefCross Ref
  39. L. S. Shapley. Additive and non-additive set functions. PhD thesis, Department of Mathematics, Princeton University, 1953.Google ScholarGoogle Scholar
  40. L. S. Shapley. A value for n-person games. In Contributions to the theory of games -- II. Princeton University Press, 1953.Google ScholarGoogle Scholar
  41. Y. Su and M. van der Schaar. Conjectural equilibrium in multiuser power control games. Transactions on Signal Processing, 57(9):3638--3650, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. Y. Su and M. van der Schaar. A new perspective on multi-user power control games in interference channels. Transactions on Wireless Communications, 8(6):2910--2919, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. T. Ui. Shapley value representation of potential games. Games and Economic Behavior, 31(1):121--135, 2000.Google ScholarGoogle ScholarCross RefCross Ref
  44. E. G. Villegas, R. V. Ferrí, and J. Josep Paradells. Frequency assignments in IEEE 802.11 WLANs with efficient spectrum sharing. Wireless Communications and Mobile Computing, 9(8):1125--1140, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. W. Willinger and J. C. Doyle. Robustness and the internet: design and evolution. In Robust design: a repertoire of biological, ecological, and engineering case studies. Oxford University Press, 2005.Google ScholarGoogle Scholar
  46. D. H. Wolpert and K. Tumer. An introduction to collective intelligence. In Handbook of Agent technology. AAAI, 1999.Google ScholarGoogle Scholar
  47. H. P. Young. Strategic Learning and its Limits. Oxford University Press, 2005.Google ScholarGoogle Scholar

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            • Published in

              cover image ACM SIGMETRICS Performance Evaluation Review
              ACM SIGMETRICS Performance Evaluation Review  Volume 38, Issue 3
              December 2010
              84 pages
              ISSN:0163-5999
              DOI:10.1145/1925019
              Issue’s Table of Contents

              Copyright © 2011 Authors

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              Association for Computing Machinery

              New York, NY, United States

              Publication History

              • Published: 3 January 2011

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