Robust equilibria in continuous games: From strategic to dynamic robustness

• URL: http://arxiv.org/abs/2512.08138v1
• Date: Tue, 09 Dec 2025 00:30:23 GMT
• Title: Robust equilibria in continuous games: From strategic to dynamic robustness
• Authors: Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet,
• Abstract summary: We examine the robustness of Nash equilibria in continuous games under both strategic and dynamic uncertainty.<n>Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness.<n>We show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces.
• Score: 25.372363445606265
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain invariant to small -- but otherwise arbitrary -- perturbations to the game's payoff structure, and we provide a crisp geometric characterization thereof. Subsequently, we turn to the question of dynamic robustness, and we examine which equilibria may arise as stable limit points of the dynamics of "follow the regularized leader" (FTRL) in the presence of randomness and uncertainty. Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness: strategic robustness implies dynamic robustness, and, conversely, the requirement of strategic robustness cannot be relaxed if dynamic robustness is to be maintained. Finally, we examine the rate of convergence to robust equilibria as a function of the underlying regularizer, and we show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces.

Related papers

• Dual-Robust Cross-Domain Offline Reinforcement Learning Against Dynamics Shifts [68.18666621908898]
  Single-domain offline reinforcement learning (RL) often suffers from limited data coverage.<n>Cross-domain offline RL handles this issue by leveraging additional data from other domains with dynamics shifts.<n>In this paper, we investigate dual (both train-time and test-time) robustness against dynamics shifts in cross-domain offline RL.
  arXiv  Detail & Related papers  (2025-12-02T07:20:39Z)
• Learnable Mixed Nash Equilibria are Collectively Rational [17.93053401419066]
  We show that uniform stability determines the last-iterate convergence behavior for the family of incremental smoothed best-response dynamics.<n>Unlike dynamics around strict equilibria, which can stabilize to socially-inefficient solutions, individually utility-seeking behaviors near mixed Nash equilibria lead to collective rationality.
  arXiv  Detail & Related papers  (2025-10-16T17:25:32Z)
• Rediscovering Entropy Regularization: Adaptive Coefficient Unlocks Its Potential for LLM Reinforcement Learning [55.59724323303857]
  We propose a framework that balances exploration and exploitation via three components: difficulty-aware coefficient allocation, initial-anchored target entropy, and dynamic global coefficient adjustment.<n>Experiments on multiple mathematical reasoning benchmarks show that AER consistently outperforms baselines, improving both reasoning accuracy and exploration capability.
  arXiv  Detail & Related papers  (2025-10-13T03:10:26Z)
• Zubov-Net: Adaptive Stability for Neural ODEs Reconciling Accuracy with Robustness [0.16355471507854133]
  We propose an adaptive stable learning framework named ZubovNet, which reformulates Zubov's equation into a consistency characterization.<n>We introduce a new paradigm for actively controlling the geometry of RoAs by directly optimizing PRoAs to reconcile accuracy and robustness.
  arXiv  Detail & Related papers  (2025-09-26T05:01:51Z)
• Critical dynamics and superconducting state preparation in the quenched Kitaev chain with pairing imbalance [0.0]
  The balance of the pairing term plays a crucial role in the emergence of topological superconductivity in the p-wave spinless Kitaev chain.<n>We investigate the effects of non-Hermitian pairing terms on both equilibrium and nonequilibrium phenomena in the Kitaev chain.
  arXiv  Detail & Related papers  (2025-09-25T20:28:58Z)
• Noradrenergic-inspired gain modulation attenuates the stability gap in joint training [44.99833362998488]
  Studies in continual learning have identified a transient drop in performance on mastered tasks when assimilating new ones, known as the stability gap.<n>We argue that it reflects an imbalance between rapid adaptation and robust retention at task boundaries.<n>Inspired by locus coeruleus mediated noradrenergic bursts, we propose uncertainty-modulated gain dynamics.
  arXiv  Detail & Related papers  (2025-07-18T16:34:06Z)
• Overcoming Non-stationary Dynamics with Evidential Proximal Policy Optimization [11.320660946946523]
  Continuous control of non-stationary environments is a major challenge for deep reinforcement learning algorithms.<n>We show that performing on-policy reinforcement learning with an evidential critic provides both.<n>We name the resulting algorithm emphEvidential Proximal Policy Optimization (EPPO) due to the integral role of evidential uncertainty quantification in both policy evaluation and policy improvement stages.
  arXiv  Detail & Related papers  (2025-03-03T12:23:07Z)
• Exploiting hidden structures in non-convex games for convergence to Nash equilibrium [62.88214569402201]
  A wide array of modern machine learning applications can be formulated as non-cooperative Nashlibria. We provide explicit convergence guarantees for both deterministic and deterministic environments.
  arXiv  Detail & Related papers  (2023-12-27T15:21:25Z)
• The equivalence of dynamic and strategic stability under regularized learning in games [33.74394172275373]
  We examine the long-run behavior of regularized, no-regret learning in finite games. We obtain an equivalence between strategic and dynamic stability. We show that methods based on entropic regularization converge at a geometric rate.
  arXiv  Detail & Related papers  (2023-11-04T14:07:33Z)
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics [41.94295877935867]
  We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion. We apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model.
  arXiv  Detail & Related papers  (2022-09-07T15:50:00Z)
• Pareto Adversarial Robustness: Balancing Spatial Robustness and Sensitivity-based Robustness [53.4380239739108]
  We design strategies to achieve universal adversarial robustness. To the best of our knowledge, we are the first to consider universal adversarial robustness via multi-objective optimization.
  arXiv  Detail & Related papers  (2021-11-03T03:28:30Z)
• Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent [55.85456985750134]
  We introduce a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting. To our best knowledge, this gives the firstever-known stability and generalization for SGD with even non-differentiable loss functions.
  arXiv  Detail & Related papers  (2020-06-15T06:30:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.