# On Existence, Mixtures, Computation and Efficiency in Multi-objective Games

arXiv: https://arxiv.org/abs/1809.04979 · HTML: https://mlsanity.com/paper/1809.04979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Preference Communication in Multi-Objective Normal-Form Games](https://mlsanity.com/paper/2111.09191/) (2021)

## Abstract (arXiv)

In a multi-objective game, each individual's payoff is a vector-valued function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing Pareto-Nash equilibria as the fundamental solution concept. In this work, we follow a classical game-theoretic agenda to study equilibria. Firstly, we show in several ways that numerous pure-strategy Pareto-Nash equilibria exist. Secondly, we propose a more consistent extension to mixed-strategy equilibria. Thirdly, we introduce a measurement of the efficiency of multiple objectives games, which purpose is to keep the information on each objective: the multi-objective coordination ratio. Finally, we provide algorithms that compute Pareto-Nash equilibria and that compute or approximate the multi-objective coordination ratio.