---
abstract: '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.'
author:
- Anisse Ismaili
bibliography:
- 'newMOG.bib'
title: 'On Existence, Mixtures, Computation and Efficiency in Multi-objective Games'
---

Introduction
============

Game theory and microeconomics assume that individuals evaluate outcomes into scalars. However, bounded rationality can hardly be modeled consistently by agents simply comparing scalars: *“The classical theory does not tolerate the incomparability of oranges and apples.”* [@simon1955behavioral]. Money is another case of scalarization of the values of outcomes. For instance, while ‘making money’ theoretically creates value [@adam1776inquiry], the tobacco industry making money and killing approximately six 