# On the robustness of learning in games with stochastically perturbed payoff observations

arXiv: https://arxiv.org/abs/1412.6565 · HTML: https://mlsanity.com/paper/1412.6565/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2014.

## Built on by (most cited first, 7 of 7)

- [Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium](https://mlsanity.com/paper/2104.12761/) (2021)
- [Learning in nonatomic games, Part I: Finite action spaces and population games](https://mlsanity.com/paper/2107.01595/) (2021)
- [A geometric decomposition of finite games: Convergence vs. recurrence under exponential weights](https://mlsanity.com/paper/2405.07224/) (2024)
- [Accelerated regularized learning in finite N-person games](https://mlsanity.com/paper/2412.20365/) (2024)
- [The impact of uncertainty on regularized learning in games](https://mlsanity.com/paper/2506.13286/) (2025)
- [Nested replicator dynamics, nested logit choice, and similarity-based learning](https://mlsanity.com/paper/2407.17815/) (2024)
- [Multi-agent learning under uncertainty: Recurrence vs. concentration](https://mlsanity.com/paper/2512.08132/) (2025)

## Abstract (arXiv)

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent trying to adapt to an arbitrarily changing environment), we show that the stochastic dynamics under study lead to no regret almost surely, irrespective of the noise level in the player's observations. In the multi-player case, we find that dominated strategies become extinct and we show that strict Nash equilibria are stochastically stable and attracting; conversely, if a state is stable or attracting with positive probability, then it is a Nash equilibrium. Finally, we provide an averaging principle for 2-player games, and we show that in zero-sum games with an interior equilibrium, time averages converge to Nash equilibrium for any noise level.