Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
125 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the stability of the logit dynamics in population games (2307.03507v2)

Published 7 Jul 2023 in cs.GT and math.DS

Abstract: We study the asymptotic stability of the logit evolutionary dynamics in population games, possibly with multiple heterogenous populations. For general population games, we prove that, on the one hand, strict Nash equilibria are asymptotically stable under the logit dynamics for low enough noise levels, on the other hand, a globally exponentially stable logit equilibrium exists for sufficiently large noise levels. This suggests the emergence of bifurcations in population games admitting multiple strict Nash equilibria, as observed in numerous examples. We then provide sufficient conditions on the population game structure for the existence of globally asymptotically stable logit equilibria for every noise level. The considered class of monotone separable games finds applications, e.g., in routing games on series compositions of networks with parallel routes when there are multiple populations of users that differ in the reward functions.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (30)
  1. L. Cianfanelli and G. Como, “On stability of users equilibria in heterogeneous routing games,” in 2019 IEEE 58th Conference on Decision and Control (CDC).   IEEE, 2019, pp. 355–360.
  2. L. Cianfanelli, G. Como, and T. Toso, “Stability and bifurcations in transportation networks with heterogeneous users,” in 2022 IEEE 61st Conference on Decision and Control (CDC).   IEEE, 2022, pp. 6371–6376.
  3. J. G. Wardrop, “Road paper. some theoretical aspects of road traffic research.” Proceedings of the institution of civil engineers, vol. 1, no. 3, pp. 325–362, 1952.
  4. S. C. Dafermos, “The traffic assignment problem for multiclass-user transportation networks,” Transportation science, vol. 6, no. 1, pp. 73–87, 1972.
  5. M. J. Smith, “The existence, uniqueness and stability of traffic equilibria,” Transportation Research Part B: Methodological, vol. 13, no. 4, pp. 295–304, 1979.
  6. F. Farokhi, W. Krichene, A. M. Bayen, and K. H. Johansson, “A heterogeneous routing game,” in 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).   IEEE, 2013, pp. 448–455.
  7. F. Farokhi and K. H. Johansson, “A game-theoretic framework for studying truck platooning incentives,” in 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013).   IEEE, 2013, pp. 1253–1260.
  8. J. Thai, N. Laurent-Brouty, and A. M. Bayen, “Negative externalities of gps-enabled routing applications: A game theoretical approach,” in 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC).   IEEE, 2016, pp. 595–601.
  9. R. Cole, Y. Dodis, and T. Roughgarden, “Pricing network edges for heterogeneous selfish users,” in Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, 2003, pp. 521–530.
  10. L. Fleischer, K. Jain, and M. Mahdian, “Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games,” in 45th Annual IEEE Symposium on Foundations of Computer Science.   IEEE, 2004, pp. 277–285.
  11. G. Karakostas and S. G. Kolliopoulos, “Edge pricing of multicommodity networks for heterogeneous selfish users,” in FOCS, vol. 4, 2004, pp. 268–276.
  12. P. Marcotte and D. Zhu, “Existence and computation of optimal tolls in multiclass network equilibrium problems,” Operations Research Letters, vol. 37, no. 3, pp. 211–214, 2009.
  13. D. Schmeidler, “Equilibrium points of nonatomic games,” Journal of statistical Physics, vol. 7, no. 4, pp. 295–300, 1973.
  14. I. Milchtaich, “Topological conditions for uniqueness of equilibrium in networks,” Mathematics of Operations Research, vol. 30, no. 1, pp. 225–244, 2005.
  15. T. Roughgarden and É. Tardos, “How bad is selfish routing?” Journal of the ACM (JACM), vol. 49, no. 2, pp. 236–259, 2002.
  16. T. Roughgarden, “The price of anarchy is independent of the network topology,” Journal of Computer and System Sciences, vol. 67, no. 2, pp. 341–364, 2003.
  17. T. Roughgarden and É. Tardos, “Bounding the inefficiency of equilibria in nonatomic congestion games,” Games and economic behavior, vol. 47, no. 2, pp. 389–403, 2004.
  18. S. C. Dafermos, “Toll patterns for multiclass-user transportation networks,” Transportation science, vol. 7, no. 3, pp. 211–223, 1973.
  19. J. Hofbauer and K. Sigmund, “Evolutionary game dynamics,” Bulletin of the American mathematical society, vol. 40, no. 4, pp. 479–519, 2003.
  20. L. E. Blume, “The statistical mechanics of strategic interaction,” Games and economic behavior, vol. 5, no. 3, pp. 387–424, 1993.
  21. J. Hofbauer, “From Nash and Brown to maynard smith: equilibria, dynamics and ess,” Selection, vol. 1, no. 1-3, pp. 81–88, 2001.
  22. M. J. Fox and J. S. Shamma, “Population games, stable games, and passivity,” Games, vol. 4, no. 4, pp. 561–583, 2013.
  23. J. Hofbauer and W. H. Sandholm, “Stable games and their dynamics,” Journal of Economic theory, vol. 144, no. 4, pp. 1665–1693, 2009.
  24. A. Blum, E. Even-Dar, and K. Ligett, “Routing without regret: On convergence to nash equilibria of regret-minimizing algorithms in routing games,” in Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing, 2006, pp. 45–52.
  25. S. Fischer and B. Vöcking, “On the evolution of selfish routing,” in European Symposium on Algorithms.   Springer, 2004, pp. 323–334.
  26. S. Jafarpour, P. Cisneros-Velarde, and F. Bullo, “Weak and semi-contraction for network systems and diffusively coupled oscillators,” IEEE Transactions on Automatic Control, vol. 67, no. 3, pp. 1285–1300, 2021.
  27. E. Lovisari, G. Como, and K. Savla, “Stability of monotone dynamical flow networks,” in 53rd IEEE Conference on Decision and Control.   IEEE, 2014, pp. 2384–2389.
  28. M. Beckmann, C. B. McGuire, and C. B. Winsten, “Studies in the economics of transportation,” Tech. Rep., 1956.
  29. G. Como and R. Maggistro, “Distributed dynamic pricing of multiscale transportation networks,” IEEE Transactions on Automatic Control, 2021.
  30. W. H. Sandholm, “Evolutionary implementation and congestion pricing,” The Review of Economic Studies, vol. 69, no. 3, pp. 667–689, 2002.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now