# Learning Nash Equilibria in Monotone Games

## TL;DR

This paper introduces a distributed algorithm for learning Nash equilibria in monotone games, requiring only local cost evaluations and converging under mild monotonicity assumptions, broadening applicability.

## Contribution

It presents a novel distributed method that guarantees convergence in monotone games without needing strong monotonicity, unlike previous algorithms.

## Key findings

- Algorithm converges under mere monotonicity.
- Applicable to games with linear coupling constraints.
- Broadens the class of games where Nash equilibria can be learned.

## Abstract

We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at each joint played action, lacking any information of the functional form of her cost or other agents' costs or strategy sets. In contrast to past work where convergent algorithms required strong monotonicity, we prove algorithm convergence under mere monotonicity assumption. This significantly widens algorithm's applicability, such as to games with linear coupling constraints.