# A utility-based analysis of equilibria in multi-objective normal form games

arXiv: https://arxiv.org/abs/2001.08177 · HTML: https://mlsanity.com/paper/2001.08177/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 9 of 9)

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- [Expected Scalarised Returns Dominance: A New Solution Concept for Multi-Objective Decision Making](https://mlsanity.com/paper/2106.01048/) (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)
- [Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation](https://mlsanity.com/paper/2508.14705/) (2025)
- [AETDICE: Unified Framework and Offline Optimization for Nonlinear Multi-Objective RL](https://mlsanity.com/paper/2606.31178/) (2026)

## Abstract (arXiv)

In multi-objective multi-agent systems (MOMAS), agents explicitly consider the possible tradeoffs between conflicting objective functions. We argue that compromises between competing objectives in MOMAS should be analysed on the basis of the utility that these compromises have for the users of a system, where an agent's utility function maps their payoff vectors to scalar utility values. This utility-based approach naturally leads to two different optimisation criteria for agents in a MOMAS: expected scalarised returns (ESR) and scalarised expected returns (SER). In this article, we explore the differences between these two criteria using the framework of multi-objective normal form games (MONFGs). We demonstrate that the choice of optimisation criterion (ESR or SER) can radically alter the set of equilibria in a MONFG when non-linear utility functions are used.