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On the Stability of the Logit Dynamics in Population Games

Cianfanelli, Leonardo and Como, Giacomo LU (2025) In IEEE Transactions on Automatic Control 70(9). p.5910-5925
Abstract

We analyze the stability of the logit evolutionary dynamics in population games, possibly with multiple heterogeneous 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 characterize a novel class of monotone separable population games for which globally asymptotically stable logit equilibria are proved to exist for every noise level. The considered class... (More)

We analyze the stability of the logit evolutionary dynamics in population games, possibly with multiple heterogeneous 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 characterize a novel class of monotone separable population games for which globally asymptotically stable logit equilibria are proved to exist 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 function.

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author
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type
Contribution to journal
publication status
published
subject
keywords
Evolutionary game theory, game theory, logit dynamics, Nash equilibrium, population games, stability
in
IEEE Transactions on Automatic Control
volume
70
issue
9
pages
16 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:105000393989
ISSN
0018-9286
DOI
10.1109/TAC.2025.3553096
language
English
LU publication?
yes
id
931ad923-fb14-41fd-8822-20145ef7b83a
date added to LUP
2025-12-19 13:27:51
date last changed
2025-12-19 13:28:27
@article{931ad923-fb14-41fd-8822-20145ef7b83a,
  abstract     = {{<p>We analyze the stability of the logit evolutionary dynamics in population games, possibly with multiple heterogeneous 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 characterize a novel class of monotone separable population games for which globally asymptotically stable logit equilibria are proved to exist 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 function.</p>}},
  author       = {{Cianfanelli, Leonardo and Como, Giacomo}},
  issn         = {{0018-9286}},
  keywords     = {{Evolutionary game theory; game theory; logit dynamics; Nash equilibrium; population games; stability}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{5910--5925}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{On the Stability of the Logit Dynamics in Population Games}},
  url          = {{http://dx.doi.org/10.1109/TAC.2025.3553096}},
  doi          = {{10.1109/TAC.2025.3553096}},
  volume       = {{70}},
  year         = {{2025}},
}