# Opponent Learning Awareness and Modelling in Multi-Objective Normal Form Games

arXiv: https://arxiv.org/abs/2011.07290 · HTML: https://mlsanity.com/paper/2011.07290/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [MOMAland: A Set of Benchmarks for Multi-Objective Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2407.16312/) (2024)
- [Preference Communication in Multi-Objective Normal-Form Games](https://mlsanity.com/paper/2111.09191/) (2021)
- [Exploring the Impact of Tunable Agents in Sequential Social Dilemmas](https://mlsanity.com/paper/2101.11967/) (2021)
- [Methods and Mechanisms for Interactive Novelty Handling in Adversarial Environments](https://mlsanity.com/paper/2302.14208/) (2023)

## Abstract (arXiv)

Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore, it is essential for an agent to learn about the behaviour of other agents in the system. In this work, we present the first study of the effects of such opponent modelling on multi-objective multi-agent interactions with non-linear utilities. Specifically, we consider two-player multi-objective normal form games with non-linear utility functions under the scalarised expected returns optimisation criterion. We contribute novel actor-critic and policy gradient formulations to allow reinforcement learning of mixed strategies in this setting, along with extensions that incorporate opponent policy reconstruction and learning with opponent learning awareness (i.e., learning while considering the impact of one's policy when anticipating the opponent's learning step). Empirical results in five different MONFGs demonstrate that opponent learning awareness and modelling can drastically alter the learning dynamics in this setting. When equilibria are present, opponent modelling can confer significant benefits on agents that implement it. When there are no Nash equilibria, opponent learning awareness and modelling allows agents to still converge to meaningful solutions that approximate equilibria.