Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Robust Equilibria in Continuous Games: From Strategic to Dynamic Robustness
Authors: Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | 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. Our contributions in the context of related work. Aiming for the strongest possible definition of robustness, we propose the following strategic refinement criterion: An equilibrium of a continuous game is strategically robust if it remains an equilibrium in any slightly perturbed, nearby game. ... Our first main result is that strategic robustness implies dynamic robustness... To the best of our knowledge, this is the first result of its kind for general continuous games. The paper is primarily focused on theoretical contributions, including definitions, characterizations, and proofs, without presenting empirical studies or experimental results. |
| Researcher Affiliation | Academia | Kyriakos Lotidis Stanford University EMAIL, Panayotis Mertikopoulos Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP LIG 38000 Grenoble, France EMAIL, Nicholas Bambos Stanford University EMAIL, Jose Blanchet Stanford University EMAIL. All listed affiliations (Stanford University, Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP LIG) are academic institutions or public research organizations. |
| Pseudocode | No | The paper describes algorithms such as Follow The Regularized Leader (FTRL) and Single-Point Stochastic Approximation (SPSA) using mathematical formulations and descriptive text, for example: 'The corresponding update rule hinges on the notion of a regularized best response, and proceeds as y_t+1 = y_t + gamma*v_hat_t, x_t = Q(y_t) for t=1,2,... (FTRL)' and 'The gradient vector is, then, estimated via the single-point stochastic approximation scheme: v_hat_i,t = (d_i/epsilon_t) u_i(x_hat_t) w_i,t (SPSA)'. However, it does not include any formally labeled 'Pseudocode' or 'Algorithm' blocks or figures. |
| Open Source Code | No | The paper does not contain any statements about releasing code, nor does it provide links to any code repositories or mention code in supplementary materials. |
| Open Datasets | No | The paper is theoretical and focuses on continuous games and Nash equilibria. It does not conduct experiments that would involve the use of any datasets, public or otherwise. |
| Dataset Splits | No | The paper is theoretical and does not involve experimental evaluation using datasets, thus no dataset splits are discussed or specified. |
| Hardware Specification | No | The paper is theoretical and does not present any experimental results. Therefore, there is no mention of specific hardware used for computations or experiments. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental setup that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup, hyperparameter values, or training configurations. |