Skip to main content

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSCONTROL))

  • 1372 Accesses

Abstract

In noncooperative games, players are self-interested and aim to maximize their own utilities. The selfishness makes the decision-making of players naturally distributed. This attractive feature is evident in a large number of game theoretic learning algorithms, e.g., better and best reply dynamics. As a result, game theoretic learning provides a powerful arsenal for the synthesis of efficient distributed algorithms to multi-agent networks. This chapter will discuss one of its applications to sensor deployment.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See [4] for a definition of proximity graph.

References

  1. R.W. Rosenthal, A class of games possessing pure strategy Nash equilibria. Int. J. Game Theory 2(1), 65–67 (1973)

    Article  MATH  Google Scholar 

  2. J.R. Marden, J.S. Shamma, Revisiting log-linear learning: asynchrony, completeness and payoff-based implementation. Games Econ Behav. 72(2), 788–808 (2012)

    Article  MathSciNet  Google Scholar 

  3. J.R. Marden, H.P. Young, G. Arslan, J.S. Shamma, Payoff based dynamics for multi-player weakly acyclic games. SIAM J. Control Optim. 48(1), 373–396 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. F. Bullo, J. Cortés, S. Martínez, Distributed Control of Robotic Networks. Applied Mathematics Series (Princeton University Press, Princeton, 2009). Available at http://www.coordinationbook.info

  5. C.B. Margi, V. Petkov, K. Obraczka, R. Manduchi, Characterizing energy consumption in a visual sensor network testbed, in International Conference on Testbeds and Research Infrastructures for the Development of Networks and Communities, pp. 332–339, March 2006

    Google Scholar 

  6. C. Vu, Distributed energy-efficient solutions for area coverage problems in wireless sensor networks. Ph.D. thesis, Georgia State University (2007)

    Google Scholar 

  7. S. Boyd, A. Ghosh, B. Prabhakar, D. Shah, Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. H.P. Young, The evolution of conventions. Econometrica 61, 57–84 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. D. Isaacson, R. Madsen, Markov Chains (Wiley, New York, 1976)

    MATH  Google Scholar 

  10. S. Anily, A. Federgruen, Ergodicity in parametric nonstationary Markov chains: an application to simulated annealing methods. Oper. Res. 35(6), 867–874 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Gidas, Nonstationary Markov chains and convergence of the annealing algorithm. J. Stat. Phys. 39(1), 73–131 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Mitra, F. Romeo, A. Sangiovanni-Vincentelli, Convergence and finite-time behavior of simulated annealing. Adv. Appl. Probab. 18(3), 747–771 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Freidlin, A. Wentzell, Random Perturbations of Dynamical Systems (Springer, New York, 1984)

    Book  MATH  Google Scholar 

  14. R.S. Sutton, A.G. Barto, Reinforcement Learning: An Introduction (MIT Press, Cambridge, 1998)

    Google Scholar 

  15. J. O’Rourke, Art Gallery Theorems and Algorithms (Oxford University Press, New York, 1987)

    MATH  Google Scholar 

  16. T.C. Shermer, Recent results in art galleries. Proc. IEEE 80(9), 1384–1399 (1992)

    Article  Google Scholar 

  17. J. Urrutia, Art gallery and illumination problems, in Handbook of Computational Geometry, ed. by J.R. Sack, J. Urrutia (North-Holland, 2000), pp. 973–1027

    Google Scholar 

  18. A. Ganguli, J. Cortés, F. Bullo, Visibility-based multi-agent deployment in orthogonal environments, in American Control Conference, New York, pp. 3426–3431, July 2007

    Google Scholar 

  19. A. Ganguli, J. Cortés, F. Bullo, Multirobot rendezvous with visibility sensors in nonconvex environments. IEEE Trans. Robot. 25(2), 340–352 (2009)

    Article  Google Scholar 

  20. J. Cortés, S. Martínez, F. Bullo, Spatially-distributed coverage optimization and control with limited-range interactions. ESAIM: Control Optim. Calc. Var. 11, 691–719 (2005)

    Google Scholar 

  21. I.F. Akyildiz, T. Melodia, K. Chowdhury, Wireless multimedia sensor networks: a survey. IEEE Trans. Wirel. Commun. 14(6), 32–39 (2007)

    Article  Google Scholar 

  22. R. Cucchiara, Multimedia surveillance systems, in Proceedings of the Third ACM International Workshop on Video Surveillance and Sensor Networks, pp. 3–10 (2005)

    Google Scholar 

  23. K.Y. Chow, K.S. Lui, E.Y. Lam, Maximizing angle coverage in visual sensor networks, in IEEE International Conference on Communications, pp. 3516–3521, June 2007

    Google Scholar 

  24. E. Hörster, R. Lienhart, On the optimal placement of multiple visual sensors, in ACM International Workshop on Video Surveillance and Sensor Networks, pp. 111–120, 2006

    Google Scholar 

  25. T. Basar, G. Olsder, Dynamic Noncooperative Game Theory. SIAM Classics in Applied Mathematics (1999)

    Google Scholar 

  26. D. Fudenberg, D. Levine, The Theory of Learning in Games (MIT Press, Cambridge, 1998)

    MATH  Google Scholar 

  27. W. Sandholm, Population Games and Evolutionary Dynamics (MIT Press, Cambridge, 2010)

    MATH  Google Scholar 

  28. H.P. Young, Individual Strategy and Social Structure (Princeton University Press, Princeton, 1998)

    Google Scholar 

  29. K.J. Arrow, G. Debreu, Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  30. J.B. Rosen, Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33(3), 520–534 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  31. F. Facchinei, C. Kanzow, Generalized Nash equilibrium problems. J. Oper. Res. 5(3), 173–210 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. J.-S. Pang, G. Scutari, F. Facchinei, C. Wang, Distributed power allocation with rate constraints in Gaussian parallel interference channels. IEEE Trans. Inf. Theory 54(8), 3471–3489 (2008)

    Article  MathSciNet  Google Scholar 

  33. H. Yin, U.V. Shanbhag, P.G. Mehta, Nash equilibrium problems with scaled congestion costs and shared constraints. IEEE Trans. Autom. Control 56(7), 1702–1708 (2011)

    Article  MathSciNet  Google Scholar 

  34. D.P. Palomar, Y.C. Eldar, Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, 2010)

    MATH  Google Scholar 

  35. A. Cortés, S. Martínez, Self-triggered best response dynamics for continuous games. IEEE Trans. Autom. Control (2013). To appear

    Google Scholar 

  36. A. Arsie, K. Savla, E. Frazzoli, Efficient routing algorithms for multiple vehicles with no explicit communications. IEEE Trans. Autom. Control 54(10), 2302–2317 (2009)

    Article  MathSciNet  Google Scholar 

  37. M. Zhu, S. Martínez, Distributed coverage games for energy-aware mobile sensor networks. SIAM J. Control Optim. 51(1), 1–27 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  38. P. Frihauf, M. Krstic, T. Basar, Nash equilibrium seeking for games with non-quadratic payoffs, in IEEE International Conference on Decision and Control, Atlanta, pp. 881-886, December 2010

    Google Scholar 

  39. S.J. Liu, M. Krstic, Stochastic Nash equilibrium seeking for games with general nonlinear payoffs. SIAM J. Control Optim. 49(4), 1659–1679 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  40. M.S. Stankovic, K.H. Johansson, D.M. Stipanovic, Distributed seeking of Nash equilibria with applications to mobile sensor networks. IEEE Trans. Autom. Control 57(4), 904–919 (2012)

    Article  MathSciNet  Google Scholar 

  41. M. Zhu, E. Frazzoli, Distributed robust adaptive equilibrium computation for generalized convex games. Automatica (2015). Accepted

    Google Scholar 

  42. M. Bardi, M. Falcone, P. Soravia, Numerical methods for pursuit-evasion games via viscosity solutions. Ann. Int. Soc. Dyn. Games 4, 105–175 (1999)

    MathSciNet  Google Scholar 

  43. R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (Dover, Mineola, 1999)

    MATH  Google Scholar 

  44. M. Bardi, I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Birkhäuser, Boston, 1997)

    Book  MATH  Google Scholar 

  45. P.E. Souganidis, Two-player, zero-sum differential games and viscosity solutions. Ann. Int. Soc. Dyn. Games 4(1), 69–104 (1999)

    MathSciNet  Google Scholar 

  46. J.P. Aubin, Viability Theory (Springer, New York, 2009)

    Book  MATH  Google Scholar 

  47. J.P. Aubin, A. Bayen, P. Saint-Pierre, Viability Theory: New Directions (Springer, New York, 2011)

    Book  Google Scholar 

  48. E. Mueller, S. Yong, M. Zhu, E. Frazzoli, Anytime computation algorithms for stochastically parametric approach-evasion differential games, in IEEE/RSJ International Conference on Intelligent Robots and Systems (Tokyo, Japan, 2013), pp. 3816–3821

    Google Scholar 

  49. J. Lygeros, On reachability and minimum cost optimal control. Automatica 40(6), 917–927 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  50. I. Mitchell, A. Bayen, C. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7), 947–957 (2005)

    Article  MathSciNet  Google Scholar 

  51. M. Huang, P. Caines, P. Malhame, Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized epsilon-Nash equilibria. IEEE Trans. Autom. Control 52(9), 1560–1571 (2007)

    Article  MathSciNet  Google Scholar 

  52. J. Lasry, P. Lions, Mean field games. Jpn. J. Math. 2(1), 229–260 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  53. J. Tembine, Q. Zhu, T. Basar, Risk-sensitive mean field games. IEEE Trans. Autom. Control 59(4), 835–850 (2014)

    Article  MathSciNet  Google Scholar 

  54. H. Yin, P. Mehta, S. Meyn, U. Shanbhag, Synchronization of coupled oscillators is a game. IEEE Trans. Autom. Control 57(4), 920–935 (2012)

    Article  MathSciNet  Google Scholar 

  55. J.R. Marden, G. Arslan, J.S. Shamma, Cooperative control and potential games. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 39(6), 1393–1407 (2009)

    Article  Google Scholar 

  56. J. Marden, A. Wierman, Overcoming the limitations of utility design for multiagent systems. IEEE Trans. Autom. Control 58(6), 1402–1415 (2013)

    Article  MathSciNet  Google Scholar 

  57. N. Li, J. Marden, Designing games for distributed optimization. IEEE J. Sel. Top. Signal Process. 7(2), 230–242 (2013)

    Article  Google Scholar 

  58. M. Zhu, M. Otte, P. Chaudhari, E. Frazzoli, Game theoretic controller synthesis for multi-robot motion planning—part I: trajectory based algorithms, in IEEE International Conference on Robotics and Automation, Hong Kong, China, pp. 1646–1651, May 2014

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Minghui Zhu .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 The Author(s)

About this chapter

Cite this chapter

Zhu, M., Martínez, S. (2015). Game Theoretic Optimal Sensor Deployment. In: Distributed Optimization-Based Control of Multi-Agent Networks in Complex Environments. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-19072-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19072-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19071-6

  • Online ISBN: 978-3-319-19072-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics