# Aspiration-based Perturbed Learning Automata in Games with Noisy Utility Measurements. Part A: Stochastic Stability in Non-zero-Sum Games

arXiv: https://arxiv.org/abs/2511.11602 · HTML: https://mlsanity.com/paper/2511.11602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 58 references that are in the map.
- First posted on arXiv 31 Oct 2025.

## Builds on (most cited first, 1 of 1)

- [Decentralized Q-Learning for Stochastic Teams and Games](https://mlsanity.com/paper/1506.07924/) (2015)

## Abstract (arXiv)

Reinforcement-based learning has attracted considerable attention both in modeling human behavior as well as in engineering, for designing measurement- or payoff-based optimization schemes. Such learning schemes exhibit several advantages, especially in relation to filtering out noisy observations. However, they may exhibit several limitations when applied in a distributed setup. In multi-player weakly-acyclic games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. To address this main limitation, this paper introduces a novel payoff-based learning scheme for distributed optimization, namely aspiration-based perturbed learning automata (APLA). In this class of dynamics, and contrary to standard reinforcement-based learning schemes, each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility games under the presence of noisy observations. This is the first part of the paper that characterizes stochastic stability in generic non-zero-sum games by establishing equivalence of the induced infinite-dimensional Markov chain with a finite dimensional one. In the second part, stochastic stability is further specialized to weakly acyclic games.