# Leveraging Noisy Observations in Zero-Sum Games

arXiv: https://arxiv.org/abs/2402.02861 · HTML: https://mlsanity.com/paper/2402.02861/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 7 of 7)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Finding Mixed Nash Equilibria of Generative Adversarial Networks](https://mlsanity.com/paper/1811.02002/) (2018)
- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)
- [Robust Reinforcement Learning as a Stackelberg Game via Adaptively-Regularized Adversarial Training](https://mlsanity.com/paper/2202.09514/) (2022)
- [On Stackelberg Mixed Strategies](https://mlsanity.com/paper/1705.07476/) (2017)
- [Beyond Local Nash Equilibria for Adversarial Networks](https://mlsanity.com/paper/1806.07268/) (2018)
- [On the commitment value and commitment optimal strategies in bimatrix games](https://mlsanity.com/paper/1612.08888/) (2016)

## Abstract (arXiv)

This paper studies an instance of zero-sum games in which one player (the leader) commits to its opponent (the follower) to choose its actions by sampling a given probability measure (strategy). The actions of the leader are observed by the follower as the output of an arbitrary channel. In response to that, the follower chooses its action based on its current information, that is, the leader's commitment and the corresponding noisy observation of its action. Within this context, the equilibrium of the game with noisy action observability is shown to always exist and the necessary conditions for its uniqueness are identified. Interestingly, the noisy observations have important impact on the cardinality of the follower's set of best responses. Under particular conditions, such a set of best responses is proved to be a singleton almost surely. The proposed model captures any channel noise with a density with respect to the Lebesgue measure. As an example, the case in which the channel is described by a Gaussian probability measure is investigated.