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An Incentive Mechanism for Agents Playing Competitive Aggregative Games

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Book cover Network Games, Control, and Optimization (NETGCOOP 2016)

Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

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Abstract

We propose an incentive mechanism for steering the strategies of noncooperative heterogeneous agents, each with strongly convex cost function depending on the average among the agents’ strategies, and all sharing a convex constraint, toward a competitive aggregative equilibrium. We consider a coordinator agent having access to the average among the agents’ strategies and broadcasting incentive signals that affect the decentralized optimal responses of the agents. Our mechanism ensures, based on the Picard–Banach fixed point iteration, global convergence to an equilibrium.

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References

  1. J. Barrera and A. Garcia. Dynamic incentives for congestion control. IEEE Trans. on Automatic Control, 60(2):299–310, 2015.

    Article  MathSciNet  Google Scholar 

  2. H. H. Bauschke and P. L. Combettes. Convex analysis and monotone operator theory in Hilbert spaces. Springer, 2010.

    MATH  Google Scholar 

  3. H. H. Bauschke, V. Martín-Márquez, S. M. Moffat, and X. Wang. Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular. Fixed Point Theory and Applications, 53:1–11, 2012.

    MathSciNet  MATH  Google Scholar 

  4. P. Combettes. Fejér monotonicity in convex optimization. In Encyclopedia of Optimization. Springer, 2000.

    Google Scholar 

  5. Andres Cortés and Sonia Martínez. Self-triggered best-response dynamics for continuous games. IEEE Trans. on Automatic Control, 60(4):1115–1120, 2015.

    Article  MathSciNet  Google Scholar 

  6. P. Dubey, O. Haimanko, and A. Zapechelnyuk. Strategic complements and substitutes, and potential games. Games and Economic Behavior, 54:77–94, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Facchinei and C. Kanzow. Generalized Nash equilibrium problems. A Quarterly Journal of Operations Research, Springer, 5:173–210, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Facchinei and J.S. Pang. Finite-dimensional variational inequalities and complementarity problems. Springer Verlag, 2003.

    MATH  Google Scholar 

  9. S. Grammatico. Aggregative control of competitive agents with coupled quadratic costs and shared constraints. In Proc. of the IEEE Conf. on Decision and Control, Las Vegas, USA, 2016.

    Google Scholar 

  10. S. Grammatico. Aggregative control of large populations of noncooperative agents. In Proc. of the IEEE Conf. on Decision and Control, Las Vegas, USA, 2016.

    Google Scholar 

  11. S. Grammatico. Dynamic control of agents playing aggregative games. IEEE Trans. on Automatic Control (submitted, https://arxiv.org/pdf/1609.08962.pdf), 2016.

  12. S. Grammatico. Exponentially convergent decentralized charging control for large populations of plug-in electric vehicles. In Proc. of the IEEE Conf. on Decision and Control, Las Vegas, USA, 2016.

    Google Scholar 

  13. S. Grammatico, B. Gentile, F. Parise, and J. Lygeros. A mean field control approach for demand side management of large populations of thermostatically controlled loads. In Proc. of the IEEE European Control Conference, Linz, Austria, 2015.

    Google Scholar 

  14. S. Grammatico, F. Parise, M. Colombino, and J. Lygeros. Decentralized convergence to Nash equilibria in constrained deterministic mean field control. IEEE Trans. on Automatic Control, http://dx.doi.org/10.1109/TAC.2015.2513368, 2016.

  15. S. Grammatico, F. Parise, and J. Lygeros. Constrained linear quadratic deterministic mean field control: Decentralized convergence to Nash equilibria in large populations of heterogeneous agents. Proc. of the IEEE Conf. on Decision and Control, pages 4412–4417, 2015.

    Google Scholar 

  16. J. S. 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.

    Article  MathSciNet  Google Scholar 

  17. J. Koshal, A. Nedić, and U. Shanbhag. Distributed algorithms for aggregative games on graphs. Operations Research, 64(3):680–704, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. N. S. Kukushkin. Best response dynamics in finite games with additive aggregation. Games and Economic Behavior, 48(1):94–10, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  19. A. A. Kulkarni and U. Shanbhag. On the variational equilibrium as a refinement of the generalized Nash equilibrium. Automatica, 48:45–55, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  20. N. Li, L. Chen, and M. A. Dahleh. Demand response using linear supply function bidding. IEEE Trans. on Smart Grid, 6(4):1827–1838, 2015.

    Article  Google Scholar 

  21. S. Li, W. Zhang, J. Lian, and K. Kalsi. Market-based coordination of thermostatically controlled loads - Part I: A mechanism design formulation. IEEE Trans. on Power Systems, 31(2):1170–1178, 2016.

    Article  Google Scholar 

  22. Z. Ma, D.S. Callaway, and I.A. Hiskens. Decentralized charging control of large populations of plug-in electric vehicles. IEEE Trans. on Control Systems Technology, 21(1):67–78, 2013.

    Article  Google Scholar 

  23. Z. Ma, S. Zou, L. Ran, X. Shi, and I. Hiskens. Efficient decentralized coordination of large-scale plug-in electric vehicle charging. Automatica, 69:35–47, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  24. J.R. Marden, G. Arslan, and J.S. Shamma. Joint strategy fictitious play with inertia for potential games. IEEE Trans. on Automatic Control, 54(2):208–220, 2009.

    Article  MathSciNet  Google Scholar 

  25. A.-H. Mohsenian-Rad, V.W.S. Wong, J. Jatskevich, R. Schober, and A. Leon-Garcia. Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Trans. on Smart Grid, 1(3):320–331, 2010.

    Article  Google Scholar 

  26. F. Parise, M. Colombino, S. Grammatico, and J. Lygeros. Mean field constrained charging policy for large populations of plug-in electric vehicles. In Proc. of the IEEE Conference on Decision and Control, pages 5101–5106, Los Angeles, California, USA, 2014.

    Google Scholar 

  27. F. Parise, B. Gentile, S. Grammatico, and J. Lygeros. Network aggregative games: Distributed convergence to Nash equilibria. In Proc. of the IEEE Conference on Decision and Control, pages 2295–2300, Osaka, Japan, 2015.

    Google Scholar 

  28. L. Pavel. An extension of duality to a game-theoretic framework. Automatica, 43:226–237, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  29. J.B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33:520–534, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  30. R.T. Rockafellar and R.J.B. Wets. Variational Analysis. Springer, 1998.

    Book  MATH  Google Scholar 

  31. W. Saad, Z. Han, H.V. Poor, and T. Başar. Game theoretic methods for the smart grid. IEEE Signal Processing Magazine, pages 86–105, 2012.

    Google Scholar 

  32. S. Uryasev and R.Y. Rubinstein. On relaxation algorithms in computation of non-cooperative equilibria. IEEE Trans. on Automatic Control, 39(6):1263–1267, 1994.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  34. M. Zhu and E. Frazzoli. Distributed robust adaptive equilibrium computation for generalized convex games. Automatica, 63:82–91, 2016.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Control Systems Group, Eindhoven University of Technology, 5612 AJ, Eindhoven, The Netherlands

    Sergio Grammatico

Authors
  1. Sergio Grammatico
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Correspondence to Sergio Grammatico .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France

    Samson Lasaulce

  2. Université d’Avignon, Laboratoire Informatique d’Avignon Université d’Avignon, Avignon cedex 9, France

    Tania Jimenez

  3. School of Mathematical Sciences, Tel Aviv University School of Mathematical Sciences, Tel Aviv, Israel

    Eilon Solan

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Grammatico, S. (2017). An Incentive Mechanism for Agents Playing Competitive Aggregative Games. In: Lasaulce, S., Jimenez, T., Solan, E. (eds) Network Games, Control, and Optimization. NETGCOOP 2016. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51034-7_11

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